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.

About the Author
Tim Hsu, San Jose State University, CA.

Reviews
"-;This is an interesting take on the second course in analysis: rather than the Lebesgue integral, we study Fourier analysis and applications. The book is well done and makes a strong case for this approach. The Introduction (which is the Introduction for the Instructor) is one of the best I.ve read, and you should definitely study if you are considering adopting the book. It explains very clearly the goals of the book, the limitations of this approach, and some other unusual features of the book." - Allen Stenger, MAA Reviews



Book Information
ISBN 9781470476007
Author Tim Hsu
Format Paperback
Page Count 354
Imprint American Mathematical Society
Publisher American Mathematical Society