Fourier Series, Fourier Transforms, and Function Spaces
eBook - PDF

Fourier Series, Fourier Transforms, and Function Spaces

A Second Course in Analysis

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Fourier Series, Fourier Transforms, and Function Spaces

A Second Course in Analysis

About this book

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.

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Table of contents

  1. Cover
  2. Title page
  3. Copyright
  4. Contents
  5. Introduction
  6. Chapter 1. Overture
  7. Part 1 Complex functions of a real variable
  8. Part 2 Fourier series and Hilbert spaces
  9. Part 3 Operators and differential equations
  10. Part 4 The Fourier transform and beyond
  11. Appendices

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Yes, you can access Fourier Series, Fourier Transforms, and Function Spaces by Tim Hsu in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.