Topics in Pure and Applied Mathematics

Course notes supplied throughout the course.

Basic background reference (title not stated in outline): https://link.springer.com/book/10.1007/978-0-387-09494-6

Ingrid Daubechies, Ten Lectures on Wavelets.

H. Dym and H. P. McKean, Fourier Series and Integrals.

G. B. Folland, Fourier Analysis and Its Applications.

G. B. Folland, Real Analysis: Modern Techniques and Their Applications.

T. W. Korner, Fourier Analysis.

W. Rudin, Real and Complex Analysis.

W. Rudin, Functional Analysis.

E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.

Yves Meyer, Wavelets and Operators.

Listed textbook (requirement not stated): Barbara D. MacCluer. Elementary Functional Analysis. Springer, 2009. Chapters 1–4.

Reference (not explicitly required): H. Brezis. Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, 2011.

Reference (not explicitly required): Avner Friedman. Foundations of Modern Analysis. Dover, 2003.

Reference (not explicitly required): Elias M. Stein and Rami Shakarchi. Functional Analysis: Introduction to Further Topics in Analysis. Princeton, 2011.

Ingrid Daubechies, Ten Lectures on Wavelets.

H. Dym and H. P. McKean, Fourier Series and Integrals.

G. B. Folland, Fourier Analysis and Its Applications.

G. B. Folland, Real Analysis: Modern Techniques and Their Applications.

T. W. Korner, Fourier Analysis.

W. Rudin, Real and Complex Analysis.

W. Rudin, Functional Analysis.

E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.

Yves Meyer, Wavelets and Operators.

M. S. Birman, M. Z. Solomjak, Spectral Theory of Self-Adjoint Operators in Hilbert Space.

Complete instructor course notes.

Lecture scripts and notebooks: https://github.com/jbramburger/DataDrivenDynSyst

Elementary Functional Analysis by Barbara D. MacCluer, Springer.

Functional Analysis, Sobolev Spaces and Partial Differential Equations by H. Brezis, Springer, 2011.

Foundations of Modern Analysis by Avner Friedman, Dover, 2003.

Functional Analysis: Introduction to Further Topics in Analysis by Elias M. Stein & Rami Shakarchi, Princeton, 2011.

H. Dym and H. P. McKean, Fourier Series and Integrals.

G. B. Folland, Fourier Analysis and Its Applications.

G. B. Folland, Real Analysis: Modern Techniques and Their Applications.

T. W. Korner, Fourier Analysis.

W. Rudin, Real and Complex Analysis.

W. Rudin, Functional Analysis.

E. M. Stein and R. Shakarchi, Functional Analysis: Introduction to Further Topics in Analysis.

P. Koosis, An Introduction to Hp Spaces.

E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces.

E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals.

E. M. Stein, Singular Integrals and Differentiability Properties of Functions.

C. Pereyra and L. Ward, Harmonic Analysis from Fourier to Wavelets.

A. Zygmund, Trigonometric Series.

Marcus, Number Fields.

Janusz, Algebraic Number Theory.

A Mathematical Introduction to Compressive Sensing by Simon Foucart and Holger Rauhut. Springer, 2013.

Sparse and Redundant Representations by Michael Elad, Springer, 2010.

B. Adcock and A. C. Hansen, Compressive Imaging: Structure, Sampling, Learning, Cambridge University Press (listed as forthcoming).

Statistical Learning with Sparsity: The Lasso and Generalizations by Trevor Hastie, Robert Tibshirani, and Martin Wainwright Taylor and Francis Group, 2015.