Fourier Series, Fourier Transforms, and Function Spaces

A Second Course in Analysis

AvTim Hsu

Häftad, Engelska, 2020

Del i serien AMS/MAA Textbooks

912 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Beskrivning

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.

Produktinformation

Utgivningsdatum:2020-03-31
Format:Häftad
Språk:Engelska
Serie:AMS/MAA Textbooks
Antal sidor:354
Förlag:American Mathematical Society
ISBN:9781470476007

Utforska kategorier

Beräkning och matematisk analys inom Naturvetenskap och teknik

Mer om författaren

Tim Hsu, San Jose State University, CA.

Recensioner i media

“-;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

Innehållsförteckning

OvertureComplex functions of a real variable: Real and complex numbersComplex-valued calculusSeries of functionsFourier series and Hilbert spaces: The idea of a function spaceFourier seriesHilbert spacesConvergence of Fourier seriesOperators and differential equations: PDEs and diagonalizationOperators on Hilbert spacesEigenbases and differential equationsThe Fourier transform and beyond: The Fourier transformApplications of the Fourier transformWhat's next?Rearrangements of seriesLinear algebraBump functionsSuggestions for problemsBibliographyIndex of selected notationIndex

Mer från samma författare

Del 1731

Quilts: Central Extensions, Braid Actions, and Finite Groups

Tim Hsu

Thomas Q. Sibley

Leslie Jane Federer Vaaler, Shinko Kojima Harper

Häftad

406 kr