Packer, Judith A

Research

research overview

My area of expertise is in Operator Algebras, in particular in the type of Algebras of Operators known as von Neumann algebras, C*-algebras and L^p operator algebras. Recently, my work has emphasized the relationship between harmonic analysis, functional analysis, wavelets and operator algebras. I am interested in noncommutative geometry, specifically in those geometries arising from special triples on twisted on twisted nilpotent discrete group C*-algebras and L^p operator algebras arising from length functions. I also am interested on noncommutative quantum metric spaces.

keywords

Functional and Harmonic Analysis, C*-algebras, Wavelet and Frame Theory

Publications

selected publications

book
- Representations, Wavelets, and Frames 2008
- Challenges for the 21st century 2001
chapter
- Problems and Recent Methods in Operator; Theory. Contemporary Mathematics. 2017
- Wavelets and Graph C ∗-Algebras. 35-86. 2017
- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice. 239-272. 2008
- Fractal wavelets of Dutkay-Jorgensen type for the Sierpinski gasket space. Contemporary Mathematics. 69-88. 2008
- George Mackey 1916–2006. Contemporary Mathematics. 1-42. 2008
conference proceeding
- Noncommutative solenoids and their projective modules. Contemporary Mathematics. 35-+. 2012
- Proceedings of the analysis conference, Singapore 1986. xii+304-xii+304. 1988
journal article
- Convergence of inductive sequences of spectral triples for the spectral propinquity. Advances in Mathematics. 2024
- Spectral triples for noncommutative solenoids and a Wiener's lemma. Journal of Noncommutative Geometry. 1415-1452. 2024
- Cocycles on groupoids arising from N^k-actions. Ergodic Theory and Dynamical Systems. 3325-3356. 2022
- Decomposing the Wavelet Representation for Shifts by Wallpaper Groups. Journal of Fourier Analysis and Applications. 2021
- Generalized Gauge Actions on k-graph C*-Algebras: KMS States and Hausdorff Structure. Indiana University Mathematics Journal. 669-709. 2021

Teaching

courses taught

MATH 2001 - Introduction to Discrete Mathematics
Primary Instructor - Spring 2021
Introduces the ideas of rigor and proof through an examination of basic set theory, existential and universal quantifiers, elementary counting, discrete probability, and additional topics. Credit not granted for this course and MATH 2002.
MATH 3001 - Analysis 1
Primary Instructor - Spring 2020 / Fall 2020 / Fall 2023
Provides a rigorous treatment of the basic results from elementary Calculus. Topics include the topology of the real line, sequences of numbers, continuous functions, differentiable functions and the Riemann integral.
MATH 3430 - Ordinary Differential Equations
Primary Instructor - Fall 2021
Involves an elementary systematic introduction to first-order scalar differential equations, nth order linear differential equations, and n-dimensional linear systems of first-order differential equations. Additional topics are chosen from equations with regular singular points, Laplace transforms, phase plane techniques, basic existence and uniqueness and numerical solutions. Formerly MATH 4430.
MATH 4001 - Analysis 2
Primary Instructor - Spring 2021 / Fall 2021
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 5001.
MATH 4330 - Fourier Analysis
Primary Instructor - Spring 2019
The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics. Same as MATH 5330.

MATH 5001 - Analysis 2
Primary Instructor - Fall 2021
Provides a rigorous treatment of infinite series, sequences of functions and an additional topic chosen by the instructor (for example, multivariable analysis, the Lebesgue integral or Fourier analysis). Same as MATH 4001.

MATH 5330 - Fourier Analysis
Primary Instructor - Spring 2019
The notion of Fourier analysis, via series and integrals, of periodic and nonperiodic phenomena is central to many areas of mathematics. Develops the Fourier theory in depth and considers such special topics and applications as wavelets, Fast Fourier Transforms, seismology, digital signal processing, differential equations, and Fourier optics. Department enforced prerequisite: MATH 4001. Same as MATH 4330.

MATH 6310 - Introduction to Real Analysis 1
Primary Instructor - Fall 2018 / Fall 2022
Develops the theory of Lebesgue measure and the Lebesgue integral on the line, emphasizing the various notions of convergence and the standard convergence theorems. Applications are made to the classical L^p spaces. Department enforced prerequisite: MATH 4001. Instructor consent required for undergraduates.

MATH 6320 - Introduction to Real Analysis 2
Primary Instructor - Spring 2019 / Spring 2020
Covers general metric spaces, the Baire Category Theorem, and general measure theory, including the Radon-Nikodym and Fubini theorems. Presents the general theory of differentiation on the real line and the Fundamental Theorem of Lebesgue Calculus. Recommended prerequisite: MATH 6310. Instructor consent required for undergraduates.

MATH 8330 - Functional Analysis 1
Primary Instructor - Fall 2019 / Fall 2020 / Fall 2023
Introduces such topics as Banach spaces (Hahn-Banach theorem, open mapping theorem, etc.), operator theory (compact operators and integral equations and spectral theorem for bounded self-adjoint operators) and Banach algebras (the Gelfand theory). Department enforced prerequisites: MATH 6310 and MATH 6320. Instructor consent required for undergraduates. See also MATH 8340.

MATH 8370 - Harmonic Analysis 1
Primary Instructor - Spring 2018 / Fall 2024
Examines trigonometric series, periodic functions, diophantine approximation and Fourier series. Also covers Bohr and Stepanoff almost periodic functions, positive definite functions and the L^1 and L^2 theory of the Fourier integral. Applications to group theory and differential equations. Department enforced prerequisites: MATH 5150 and MATH 6320. Instructor consent required for undergraduates.

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