Aspects of harmonic analysis on locally compact Abelian groups - Gallier, Jean; Quaintance, Jocelyn (New Jersey : World Scientific, 2024)
The Fourier transform is a "tool" used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.
Includes bibliography, appendix, symbol index and index.
Keywords: Locally compact Abelian groups; Harmonic analysis; Fourier analysis; Measure theory