research overview
- My current research concerns finance, quantum physics, and topics in pure and applied mathematics.
- Contact Info
Gustafson, Karl E
Positions
- Professor Emerita/Emeritus, Mathematics
Research Areas
Research
keywords
- MATHEMATICAL PHYSICS, PARTIAL DIFFERENTIAL EQUATIONS, LINEAR ALGEBRA, FINANCE
Publications
selected publications
-
book
- Quantum social science 2013
- Introduction to Partial Differential Equations and Hilbert Space Methods 2012
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Antieigenvalue Analysis
2012
-
The Crossing of Heaven
2012
- Introduction to partial differential equations and Hilbert space methods 1999
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Lectures on Computational Fluid Dynamics, Mathematical Physics and Linear Algebra
1997
-
Numerical Range
1997
- Lectures on Computational Fluid Dynamics, Mathematical Physics, and Linear Algebra 1996
- Applied Partial Differential Equations 2 1992
- Applied Partial Differential Equations 1 1991
-
Vortex Methods and Vortex Motion
1991
- Introduction to partial differential equations and Hilbert space methods 1987
- Quantum Mechanics in Mathematics, Chemistry, and Physics 1981
- Introduction to partial differential equations and Hilbert space methods 1980
-
chapter
- Operator geometry in statistics. 355-382. 2011
- The Trigonometry of Twistors and Elementary Particles. AIP Conference Proceedings. 65-73. 2009
-
The operator trigonometry in statistics.
189-193.
2008
-
WAVELETS AND EXPECTATIONS: A DIFFERENT PATH TO WAVELETS.
5-22.
2007
-
NONCOMMUTATIVE TRIGONOMETRY AND QUANTUM MECHANICS.
341-360.
2007
- Navier-Stokes computation of hovering dynamics. 552-572. 2007
-
No Radial Symmetries in the Arrhenius-Semenov Thermal Explosion Equation.
357-370.
2007
- The born rule. AIP Conference Proceedings. 98-107. 2007
- Time-Space Dilations and Stochastic-Deterministic Dynamics 2007
-
Noncommutative Trigonometry.
127-155.
2006
- Bell’s inequalities and the Accardi-Gustafson inequality. 207-223. 2003
- The quantum Zeno paradox and the counter problem. 225-236. 2003
- An unconventional computational linear algebra: Operator trigonometry. 48-67. 2001
- A composition adjoint lemma. 253-258. 2000
- Semigroup theory and operator trigonometry. 131-140. 2000
- The Trigonometry of Quantum Probabilities. 159-173. 2000
- Antieigenvalues: an extended spectral theory. 144-149. 1999
- Rigged spectral states: a proclivity for eigenvalues. 48-55. 1999
- The geometry of quantum probabilities. 151-164. 1999
-
Domain decomposition, operator trigonometry, Robin condition.
Contemporary Mathematics.
432-437.
1998
- Ergodic learning algorithms. 228-242. 1998
-
From stochastic semigroups to chaotic dynamics.
Lecture Notes in Physics.
110-123.
1998
- Operator Trigonometry of Wavelet Frames 1998
- Semigroups and antieigenvalues. 379-384. 1998
- Acceleration Methods. 16-18. 1997
- Antieigenvalues. 57-57. 1997
- Singular Angles of a Square Matrix. 356-367. 1996
-
Foreword.
Advances in neuroimmunology.
1-3.
1995
- On the Computation of Periodic Solutions for Autonomous Partial Differential Equation Boundary Value Problems. 32-56. 1993
-
5. Four Principles of Vortex Motion.
95-141.
1991
- A second-order translation, rotation, and scale invariant neural network 1991
- The flow semigroup approximation problem. 343-354. 1991
- Visualization and computation of hovering mode vortex dynamics. 143-169. 1991
- Reversibility in Neural Processing Systems 1990
- A theory for computational vortex dynamics. 265-269. 1989
-
Controversies concerning finite/infinite sequences of fluid corner vortices.
Contemporary Mathematics.
351-357.
1989
- Factorization problems in fast elliptic solvers 1989
- Multigrid localization and multigrid grid generation for the computation of vortex structure and dynamics of flows in cavities and about airfoils. 229-250. 1988
- Robust multigrid computation and visualization of separation and vortex evolution in aerodynamic flows. 174-184. 1988
- Vortex Subdomains. 370-380. 1988
- INTERMITTENT BIFURCATION OF VORTEX FLOWS. Lecture Notes in Mathematics. 155-161. 1987
- Kolmogorov systems and Haar systems. 401-416. 1987
- Spectral estimation and factorization in higher dimensions. 383-399. 1987
- Combustion and explosion equations and their calculation. 161-195. 1985
- Graph theory in the approximation theory of fluid dynamics. 511-519. 1984
- On the structure of finite element solenoidal subspaces 1984
- Remarks (1983) on three new and unsolved problems (1971) in operator theory (1) Principal Axis (2) Numerical Range (3) Numerical Radius 1984
-
Vorticity, Incompressibility, and Boundary Conditions in the Numerical Solution of the Navier-Stokes Equations.
North Holland Mathematics Studies.
257-264.
1984
- A Banach-Lamperti theorem and similarity transformations in statistical mechanics. 567-579. 1983
- Hybrid fast Poisson solvers for fluid dynamics, transonic flow, solenoidal projection, and the Navier-Stokes equations for general domains. 87-96. 1983
- Irreversibility questions in chemistry, quantum-counting, and time-delay. 516-526. 1983
- Numerical calculation of critical parameters of thermal explosion 1983
- On the divergence-free (i.e., mass conservation, solenoidal) condition in computational fluid dynamics: how important is it?. 617-626. 1983
- Regular representation and approximation. 539-550. 1983
- COMPUTATION OF SOLENOIDAL (DIVERGENCE-FREE) VECTOR-FIELDS. Lecture Notes in Mathematics. 95-113. 1982
- The singular sequence problem. 289-294. 1982
- Timestep control for the numerical solutions of initial-boundary value problems 1981
- A study of the Helmholtz operator. 107-120. 1981
- Higher-dimensional spectral factorization with applications to digital filtering. 199-205. 1981
- Irreversibility and stochasticity of chemical processes 1981
- On a generalized Weyl-Von Neumann converse theorem 1981
- On the dimension of the finite difference approximations to divergence free vectors. 125-132. 1981
- Recent progress on the nonlinear Hartree-Fock, concentration-diffusion, and Navier-Stokes equations. 296-309. 1981
- Weighted trigonometric approximations in L2(Rn). 343-350. 1981
- Correlations and evolution equations. 243-Vol. 2. 1976
- Candidates for oac and Hac 1974
- Fourier Scattering Subspaces 1974
- Antieigenvalue inequalities in operator theory. 115-119. 1972
- New and unsolved problems. 493-Vol. 20. 1972
- Weyl’s theorems. 80-Vol. 20. 1972
-
conference proceeding
- Antieigenvalue Analysis, New Applications: Continuum Mechanics, Economics,Number Theory. 116-120. 2015
- The Future of Mathematics: From the Pure-Applied Debate to Reality. 113-113. 2014
-
Detailed Balance.
AIP Conference Proceedings.
2011
-
A Trigonometry of Quantum States.
AIP Conference Proceedings.
72-85.
2009
- Interconnections of Quantum, Machine, and Human Learning. 56-62. 2007
- Preconditioning, Inner Products, Normal Degree 2003
- A Zeno Story. 265-272. 2001
- Bell's Inequalities. 524-554. 2001
- Wavelets as Stochastic Processes. 40-43. 1998
- Assigning Initial Weights in Feedforward Neural Networks. 1108-1113. 1998
- Operator Trigonometry of Linear Systems. 950-955. 1998
- Capturing correct solutions in CFD. Lecture Notes in Physics. 171-176. 1998
- Some Differential Equations and Dynamical Systems and Their Applications. 22-38. 1998
- Internal Dynamics of Backpropagation Learning. 179-182. 1998
- Trigonometric Interpretation of Iterative Methods. 23-29. 1996
- Biological Aerodynamic Systems. 33-42. 1994
-
SYMMETRY-BREAKING IN CFD - CAUSES AND CONSEQUENCES.
International Journal of Modern Physics C: computational physics and physical computation.
189-194.
1993
-
MATRIX TRIGONOMETRY.
Linear Algebra and Its Applications.
117-140.
1993
- Accessing the Null Space with Nonlinear Multilayer Neural Networks. 308-316. 1992
- High Lift/High Thrust Hovering Dynamics. 116-135. 1992
- Human and machine 'quick modelling'. Advances in neural information processing systems. 1151-1158. 1992
- Semiconductor Voltage-Current Characteristics and Combustion Branching Diagrams. 230-231. 1991
- An Asymptotic Singular Value Decomposition Analysis of Nonlinear Multilayer Neural Networks. 785-789. 1991
- Vortex Patterns, Thrust, and Lift for Hovering Modes. 461-466. 1991
- Antieigenvalues in Analysis. 57-69. 1990
- Computation of Hovering Mode Vortex Dynamics. 98-102. 1990
- Connectionist Nonlinear Over-Relaxation. 179-184. 1990
- Periodicities, Intermittencies, and Criticalities inDriven Cavity and General Flows. 103-107. 1990
- Preconditioned Conjugate Gradient Algorithm for Irregular Finite Element Grids. 60-66. 1990
- Computational Vortex Dynamics: Some history, and Relation to Analytical Treatment. 257-258. 1988
- Nonblowups, Periodicities, Vortex Shreddings in Combustion and Hydrodynamic Flows: A Conference Report. 483-500. 1988
- Parameters of Hopf Bifurcation in Driven Cavity Flow. 278-281. 1988
- Viscous Flows About Airfoils. 139-144. 1988
- Vortex Dynamics of Viscous Flow Around Airfoils. 267-270. 1988
- Numerical methods for finding fluid fine structure. 5-8. 1985
- Parallel methods for heterogeneous fluid structures. 191-208. 1985
- Graph-theoretic aspects of flow computation methods. 219-224. 1984
- Mathematical physics. VII. Physica A: Statistical Mechanics and its Applications. i--ix and 1--715-i--ix and 1--715. 1984
- Scattering theory and the principle of limiting absorption. 335-349. 1978
-
journal article
-
CONDITIONS IMPLYING COMMUTATIVITY OF UNBOUNDED SELF-ADJOINT OPERATORS AND RELATED TOPICS.
Journal of Operator Theory.
159-169.
2016
-
The importance of imagination (or lack thereof) in artificial, human and quantum decision making.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
2016
-
Antieigenvalue analysis for continuum mechanics, economics, and number theory.
Special Matrices.
1-8.
2016
-
Why the Kemeny Time is a constant.
Special Matrices.
176-180.
2016
-
A new financial risk ratio.
Journal of Statistical Computation and Simulation.
2682-2692.
2015
-
Time operator of Markov chains and mixing times. Applications to financial data.
Physica A: Statistical Mechanics and its Applications.
141-155.
2014
-
Unbounded products of operators and connections to Dirac-type operators.
Bulletin des Sciences Mathematiques.
626-642.
2014
-
IMPLICIT SPACE-TIME DOMAIN DECOMPOSITION METHODS FOR STOCHASTIC PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS.
SIAM Journal on Scientific Computing.
C1-C24.
2014
- The Future of Mathematics: From the Pure-Applied Debate to Reality. 79-93. 2014
-
Financial Time Operator for random walk markets.
Chaos, Solitons and Fractals.
62-72.
2013
- Financial Time operator and the complexity of Time. Mind and Matter. 83-100. 2013
- The Summit Club. 29-32. 2013
-
On Operator Sum and Product Adjoints and Closures.
Canadian Mathematical Bulletin.
456-463.
2011
-
Trigonometry of Quantum States.
Foundations of Physics: an international journal devoted to the conceptual and fundamental theories of modern physics, biophysics, and cosmology.
450-465.
2011
-
Slant antieigenvalues and slant antieigenvectors of operators.
Linear Algebra and Its Applications.
1348-1362.
2010
-
Operator trigonometry of multivariate finance.
Journal of Multivariate Analysis.
374-384.
2010
- Experiences and Insights in Mathematical Finance. 35-41. 2010
- On my min-max theorem (1968) and its consequences. Acta et Commentationes Universitatis Tartuensis de Mathematica. 45-51. 2010
-
Operator trigonometry of Hotelling correlation, Frobenius condition, Penrose twistor.
Linear Algebra and Its Applications.
2762-2770.
2009
-
Superstochastic matrices and magic Markov chains.
Linear Algebra and Its Applications.
2705-2715.
2009
-
The Geometry of Statistical Efficiency and Matrix Statistics.
Advances in Decision Sciences.
1-16.
2007
-
Reversibility and regularity.
International Journal of Theoretical Physics.
1867-1880.
2007
- The End of the Certain World (N. Greenspan). Journal of Scientific Exploration. 416-423. 2007
-
The trigonometry of matrix statistics.
International Statistical Review.
187-202.
2006
- Meta Math! The Quest for Omega (G. Chaitin). Journal of Scientific Exploration. 332-337. 2006
-
Bell and Zeno.
International Journal of Theoretical Physics.
1933-1942.
2005
- A World Without Time (P. Yourgrau). Journal of Scientific Exploration. 274-278. 2005
-
On the eigenvalues which express antieigenvalues.
International Journal of Mathematics and Mathematical Sciences.
1543-1554.
2005
- The Geometry of Statistical Efficiency. 105-121. 2005
-
Interaction antieigenvalues.
Journal of Mathematical Analysis and Applications.
174-185.
2004
-
An inner product lemma.
Numerical Linear Algebra with Applications.
649-659.
2004
-
Normal degree.
Numerical Linear Algebra with Applications.
661-674.
2004
-
Positive dilations of piecewise monotonic Markov maps.
Infinite Dimensional Analysis Quantum Probability and related topics.
261-269.
2004
-
Probability from chaos.
International Journal of Quantum Chemistry.
150-159.
2004
-
Microscopic irreversibility.
Discrete Dynamics in Nature and Society.
155-168.
2004
- Invitation to Linear Operators (T, Furuta). SIAM Review. 167-168. 2004
-
Continued fractions, wavelet time operators, and inverse problems.
Rocky Mountain Journal of Mathematics.
661-688.
2003
-
Operator trigonometry of preconditioning, domain decomposition, sparse approximate inverses, successive overrelaxation, minimum residual schemes.
Numerical Linear Algebra with Applications.
291-315.
2003
- A Zeno Story. 35-55. 2003
- Professor Ilya Prigogine: A Personal and Scientific Remembrance. Mind and Matter. 9-13. 2003
-
Operator trigonometry of statistics and econometrics.
Linear Algebra and Its Applications.
141-158.
2002
- CP violation as antieigenvector-breaking. Advances in Chemical Physics. 239-258. 2002
- Distinguishing discretization and discrete dynamics, with application to machine learning, ecology, and atomic physics. 100-111. 2002
- The End of Time (J. Barbour). Journal of Scientific Exploration. 278-280. 2002
-
Probability, geometry, and irreversibility in quantum mechanics.
Chaos, Solitons and Fractals.
2849-2858.
2001
-
Insect flight simulation resembles Navier-Stokes.
Physics Today.
82-82.
2001
- An Unconventional Report on the Conference UMC'2K. Bulletin- European Association for Theoretical Computer Science. 186-189. 2001
-
An extended operator trigonometry.
Linear Algebra and Its Applications.
117-135.
2000
-
Quantum trigonometry.
Infinite Dimensional Analysis Quantum Probability and related topics.
33-52.
2000
-
Chaos in discrete learning systems.
Chaos, Solitons and Fractals.
321-327.
2000
-
The Time operator of wavelets.
Chaos, Solitons and Fractals.
443-452.
2000
-
Parallel computing forty years ago.
Mathematics and Computers in Simulation.
47-62.
1999
-
The geometrical meaning of the Kantorovich-Wielandt inequalities.
Linear Algebra and Its Applications.
143-151.
1999
-
Wavelets and stochastic processes.
Mathematics and Computers in Simulation.
81-104.
1999
- A computational trigonometry, and related contributions by Russians Kantorovich, Krein, Kaporin. 73-83. 1999
- Time,Temporality, Now (Atmanspacher, Ruhnau). Journal of Scientific Exploration. 695-703. 1999
-
Operator trigonometry of the model problem.
Numerical Linear Algebra with Applications.
377-399.
1998
- Haar's wavelets and differential equations. Differential Equations. 829-832. 1998
-
On the inverse problem of statistical physics: from irreversible semigroups to chaotic dynamics.
Physica A: Statistical Mechanics and its Applications.
345-361.
1998
-
(Victor) Gustave Robin: 1855-1897.
The Mathematical Intelligencer.
47-53.
1998
-
Internal sigmoid dynamics in feedforward neural networks.
Connection Science: journal of neural computing, artificial intelligence, and cognitive research.
43-73.
1998
-
The third boundary condition - Was it Robin's?.
The Mathematical Intelligencer.
63-71.
1998
-
Contextual quick-learning and generalization by humans and machines.
Network: computation in neural systems.
85-106.
1998
- Haar wavelets and differential equations. Differential Equations. 832-863. 1998
-
Operator spectral states.
Computers and Mathematics with Applications.
467-508.
1997
-
Operator trigonometry of iterative methods.
Numerical Linear Algebra with Applications.
333-347.
1997
-
From irreversible Markov semigroups to chaotic dynamics.
Physica A: Statistical Mechanics and its Applications.
296-308.
1997
-
Biological dynamical subsystems of hovering flight.
Mathematics and Computers in Simulation.
397-410.
1996
-
Qualitative features of high lift hovering dynamics and inertial manifolds.
Theoretical and Computational Fluid Dynamics.
89-104.
1996
-
A NOTE ON OPTIMAL ERGODIC INVARIANT-MEASURES FOR PIECEWISE-LINEAR MAPS ON FRACTAL REPELLERS.
Physics Letters A: General Physics, Nonlinear Science, Statistical Physics, Atomic, Molecular and Cluster Physics, Plasma and Fluid Physics, Condensed Matter, Cross-disciplinary Physics, Biological Physics, Nanosciences, Quantum Physics.
117-126.
1995
-
THEORY AND COMPUTATION OF PERIODIC-SOLUTIONS OF AUTONOMOUS PARTIAL-DIFFERENTIAL EQUATION BOUNDARY-VALUE-PROBLEMS, WITH APPLICATION TO THE DRIVEN CAVITY PROBLEM.
Mathematical and Computer Modelling.
57-75.
1995
- Gustav Robin and Pierre Duhem: A Study of Scientists Caught Within Intellectual Tyrannies. 20-27-20-27. 1995
- Gustav Robin: Evaluation of his major achievements in Thermodynamics and Potential Theory. 22-27. 1995
- ANTIEIGENVALUES. Linear Algebra and Its Applications. 437-454. 1994
-
Operator trigonometry.
Linear and Multilinear Algebra.
139-159.
1994
-
INDUCTIVE INFERENCE AND NEURAL NETS.
Network: computation in neural systems.
203-227.
1994
-
A NOTE ON TOTAL ANTIEIGENVECTORS.
Journal of Mathematical Analysis and Applications.
603-611.
1993
-
FROM PROBABILISTIC DESCRIPTIONS TO DETERMINISTIC DYNAMICS.
Physica A: Statistical Mechanics and its Applications.
153-166.
1993
- Introduction to Neural and Cognitive Modeling (D. Levine). Mathematics and Computers in Simulation. 458-460. 1993
- Iterative methods for connectionist architectures. 67-88. 1993
- Primacy and Recency Effects in Backpropagation Learning. 271-298. 1993
- Lift and Thrust Generation by an airfoil in hover modes. 47-57. 1992
-
A USEFUL ANALOGY BETWEEN SEMICONDUCTOR VOLTAGE-CURRENT CHARACTERISTICS AND COMBUSTION BRANCHING DIAGRAMS.
Compel: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering.
465-473.
1991
- COMPUTATIONAL PHYSICS - A COMMENTARY. Mathematics and Computers in Simulation. 269-272. 1991
-
COMPUTATION OF DRAGONFLY AERODYNAMICS.
Computer Physics Communications.
121-132.
1991
-
COMPUTATIONAL PHYSICS - PLENARY LECTURES AND EXPANDED SELECTED PAPERS FROM THE IMACS 1ST INTERNATIONAL-CONFERENCE ON COMPUTATIONAL PHYSICS - BOULDER, 11-15 JUNE 1990 - PREFACE.
Computer Physics Communications.
R11-R11.
1991
-
PRECONDITIONED CONJUGATE-GRADIENT AND FINITE-ELEMENT METHODS FOR MASSIVELY DATA-PARALLEL ARCHITECTURES.
Computer Physics Communications.
253-267.
1991
-
SEMICONDUCTOR-DEVICE SIMULATION.
Computer Physics Communications.
133-136.
1991
-
TIME-ASYMPTOTIC FLOW CALCULATION.
Computer Physics Communications.
107-116.
1991
- Who is Who in IMACS: K. Gustafson. Mathematics and Computers in Simulation. 263-263. 1991
-
HOPF-BIFURCATION IN THE DRIVEN CAVITY.
Journal of Computational Physics.
219-261.
1990
-
COUNTING THE NUMBER OF SOLUTIONS IN COMBUSTION AND REACTIVE FLOW PROBLEMS.
Zeitschrift fuer Angewandte Mathematik und Physik.
558-578.
1990
- Matematica Computacional y Matematicos Computacionales. 3-13. 1990
- Stochastic Processes in the Neurosciences (H. Tuckwell). SIAM Review. 318-322. 1990
-
Thrust generation by an airfoil in hover modes.
Experiments in Fluids: experimental methods and their applications to fluid flow.
17-24.
1990
-
ANTIEIGENVALUE BOUNDS.
Journal of Mathematical Analysis and Applications.
327-340.
1989
-
CAVITY FLOW DYNAMICS AT HIGHER REYNOLDS-NUMBER AND HIGHER ASPECT RATIO.
Journal of Computational Physics.
271-283.
1987
-
VORTEX SEPARATION AND FINE-STRUCTURE DYNAMICS.
Applied Numerical Mathematics.
167-182.
1987
-
SPECTRAL APPROXIMATION.
Journal of Approximation Theory.
272-293.
1986
-
MULTIGRID CALCULATION OF SUBVORTICES.
Applied Mathematics and Computation.
89-102.
1986
-
VORTEX DYNAMICS OF CAVITY FLOWS.
Journal of Computational Physics.
279-319.
1986
-
ON K-FLOWS AND IRREVERSIBILITY.
Journal of Statistical Physics.
317-320.
1986
- Computation of the fine vortex structures of fluids. 355-363. 1986
-
Principles of electricity and economics in fluid dynamics.
Numerical Methods for Partial Differential Equations.
145-157.
1985
-
A NEW METHOD FOR COMPUTING SOLENOIDAL VECTOR-FIELDS ON ARBITRARY REGIONS.
International Journal for Numerical Methods in Fluids.
763-783.
1985
-
GRAPH-THEORY AND FLUID-DYNAMICS.
643-656.
1985
-
THE CURL OF GRAPHS AND NETWORKS.
Mathematical modelling.
145-155.
1985
- MATHEMATICAL PHYSICS VII PROCEEDINGS OF THE VIITH INTERNATIONAL-CONGRESS-ON-MATHEMATICAL-PHYSICS BOULDER, COLORADO, USA AUGUST 1-10, 1983 - PREFACE. Physica A: Statistical Mechanics and its Applications. R5-R6. 1984
-
CALCULATION OF CRITICAL BRANCHING POINTS IN 2-PARAMETER BIFURCATION PROBLEMS.
Journal of Computational Physics.
171-177.
1983
-
DIVERGENCE-FREE BASES FOR FINITE-ELEMENT SCHEMES IN HYDRODYNAMICS.
SIAM Journal on Numerical Analysis.
697-721.
1983
- Hybrid fast Poisson solvers for fluid dynamics, transonic flow, solenoidal projection, and the Navier-Stokes equations for general domains. 87-96. 1983
- Non-relativistic Quantum Mechanics (W. Amrein). Bulletin of the American Mathematical Society. 477-481. 1983
- THE RKNG (RELLICH, KATO, SZ-NAGY, GUSTAFSON) PERTURBATION THEOREM FOR LINEAR-OPERATORS IN HILBERT AND BANACH-SPACE. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 201-211. 1983
-
EXACT-SOLUTIONS AND IGNITION PARAMETERS IN THE ARRHENIUS CONDUCTION THEORY OF GASEOUS THERMAL-EXPLOSION.
Zeitschrift fuer Angewandte Mathematik und Physik.
392-405.
1982
-
PARTIAL INNER PRODUCT-SPACES AND SEMI-INNER PRODUCT-SPACES.
Advances in Mathematics.
281-300.
1981
-
WEIGHTED TRIGONOMETRIC APPROXIMATION AND INNER-OUTER FUNCTIONS ON HIGHER DIMENSIONAL EUCLIDEAN SPACES.
Journal of Approximation Theory.
368-382.
1981
-
ON CONVERSE TO KOOPMANS LEMMA.
Physica A: Statistical Mechanics and its Applications.
379-388.
1980
-
ON THE EISENBUD-WIGNER FORMULA FOR TIME-DELAY.
Letters in Mathematical Physics.
381-385.
1980
- Unitary group representations in physics, probability, and number theory (G. Mackey). Bulletin of the American Mathematical Society. 225-229. 1980
- Response to query 150 S. Hastings, The Robin Boundary Condition. Notices of the American Mathematical Society. 103-228. 1979
-
NUMERICAL RANGE AND ACCRETIVITY OF OPERATOR PRODUCTS.
Journal of Mathematical Analysis and Applications.
693-702.
1977
-
Canonical commutation relations of quantum mechanics and stochastic regularity.
Letters in Mathematical Physics.
275-280.
1976
- ASYMPTOTIC-DISTRIBUTION OF EIGENVALUES OF PRODUCT OPERATORS DETERMINING HYDRODYNAMIC STABILITY. Notices of the American Mathematical Society. A682-A682. 1976
- On algebraic multiplicity. Indiana University Mathematics Journal. 769-781. 1976
- PARTICLE DECAY AND STOCHASTIC REGULARITY. Notices of the American Mathematical Society. A218-A218. 1976
- ALGEBRAIC MULTIPLICITY. Notices of the American Mathematical Society. A627-A627. 1975
- WEYL-BROWDER ALGEBRAIC ESSENTIAL SPECTRUM AND WEINSTEIN-ARONSZAJN DETERMINANT THEORY. Notices of the American Mathematical Society. A709-A709. 1975
- On operator radii. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 63-68. 1974
- On the absolutely continuous subspace of a self-adjoint operator. Annales Henri Poincare. 163-166. 1974
-
Large nonlinearities and closed linear operators.
Archive for Rational Mechanics and Analysis.
10-19.
1973
-
Some essentially self-adjoint Dirac operators with spherically symmetric potentials.
Israel Journal of Mathematics.
63-75.
1973
-
Multiplicative perturbation of semigroup generators.
Pacific Journal of Mathematics.
731-742.
1972
-
Large nonlinearities and monotonicity.
Archive for Rational Mechanics and Analysis.
109-122.
1972
- Multiplicative perturbation of nonlinear $m$-accretive operators. 149-158. 1972
- Necessary and sufficient conditions for Weyl’s theorem. Michigan Mathematical Journal. 71-81. 1972
- A branching analysis of the Hartree equation. 723-734 (1972). 1971
- Elements of Functional Analysis (I.J.Maddox). American Mathematical Monthly. 316-317. 1971
- The Toeplitz-Hausdorff theorem for linear operators. Proceedings of the American Mathematical Society. 203-204. 1970
-
Some perturbation theorems for nonnegative contraction semigroups*.
Journal of Mathematical Society of Japan.
1969
- Doubling perturbation sizes and preservation of operator indices in normed linear spaces. 281-294. 1969
- On projections of selfadjoint operators and operator product adjoints.. Bulletin of the American Mathematical Society. 739-741. 1969
- On the cosine of unbounded operators. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 33-34. 1969
- On the essential spectrum. Journal of Mathematical Analysis and Applications. 121-127. 1969
-
Compact-Like Operators and the Eberlein Theorem.
American Mathematical Monthly.
958-964.
1968
-
A note on left multiplication of semigroup generators.
Pacific Journal of Mathematics.
463-465.
1968
- A min-max theorem. Notices of the American Mathematical Society. 799-799. 1968
-
Positive (noncommuting) operator products and semigroups.
Mathematische Zeitschrift.
160-172.
1968
- State diagrams for Hilbert space operators. 33-45. 1968
- The angle of an operator and positive operator products. Bulletin of the American Mathematical Society. 488-492. 1968
-
Inequalities for Nonlocal Parabolic and Higher Order Elliptic Equations.
SIAM Review.
531-541.
1967
-
Stability Inequalities for Semimonotonically Perturbed Nonhomogeneous Boundary Problems.
SIAM Journal on Applied Mathematics.
368-391.
1967
- A perturbation lemma. Bulletin of the American Mathematical Society. 334-338. 1966
-
CONDITIONS IMPLYING COMMUTATIVITY OF UNBOUNDED SELF-ADJOINT OPERATORS AND RELATED TOPICS.
Journal of Operator Theory.
159-169.
2016
Teaching
courses taught
-
MATH 4470 - Partial Differential Equations
Primary Instructor - Fall 2018 / Spring 2019 / Fall 2019
Studies initial, boundary, and eigenvalue problems for the wave, heat, and potential equations. Solution by separation of variables, Green's function, and variational methods. Same as MATH 5470. -
MATH 5470 - Partial Differential Equations
Primary Instructor - Fall 2018 / Spring 2019 / Fall 2019
Studies initial boundary and eigenvalue problems for the wave, heat and potential equations. Solution by separation of variables, Green's function, and variational methods. Department enforced prerequisite: MATH 3430 or MATH 5430. Instructor consent required for undergraduates. Same as MATH 4470.
Background
education and training
- Ph.D., University of Maryland College Park Campus 1965
- B.S., University of Colorado Boulder 1958