Fourier Series, Fourier Transforms, and Function Spaces: A Second Course in Analysis

Tim Hsu

354 pages, parution le 29/03/2020

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Résumé

A textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces. Fourier Series, Fourier Transforms, and Function Spaces is designed as a textbook for a second course or capstone course in analysis for advanced undergraduate or beginning graduate students. By assuming the existence and properties of the Lebesgue integral, this book makes it possible for students who have previously taken only one course in real analysis to learn Fourier analysis in terms of Hilbert spaces, allowing for both a deeper and more elegant approach. This approach also allows junior and senior undergraduates to study topics like PDEs, quantum mechanics, and signal processing in a rigorous manner. Students interested in statistics (time series), machine learning (kernel methods), mathematical physics (quantum mechanics), or electrical engineering (signal processing) will find this book useful. With 400 problems, many of which guide readers in developing key theoretical concepts themselves, this text can also be adapted to self-study or an inquiry-based approach. Finally, of course, this text can also serve as motivation and preparation for students going on to further study in analysis.

Overture
Complex functions of a real variable: Real and complex numbers
Complex-valued calculus
Series of functions
Fourier series and Hilbert spaces: The idea of a function space
Fourier series
Hilbert spaces
Convergence of Fourier series
Operators and differential equations: PDEs and diagonalization
Operators on Hilbert spaces
Eigenbases and differential equations
The Fourier transform and beyond: The Fourier transform
Applications of the Fourier transform
What's next?
Rearrangements of series
Linear algebra
Bump functions
Suggestions for problems
Bibliography
Index of selected notation
Index.

Tim Hsu , San Jose State University, CA.

Caractéristiques techniques

	PAPIER
Éditeur(s)	American mathematical society
Auteur(s)	Tim Hsu
Parution	29/03/2020
Nb. de pages	354
EAN13	9781470451455

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Fourier Series, Fourier Transforms, and Function Spaces: A Second Course in Analysis

Résumé

Caractéristiques techniques

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