Foundations of Time-Frequency Analysis (Applied and Numerical Harmonic Analysis) by Karlheinz Gröchenig

by K.U. Grochening

"Time-frequency analysis is a source of ideas and applications in modern harmonic analysis. The history of time-frequency analysis dates back to von Neumann, Wigner, and Gabor, who considered the problems in quantum mechanics and in information theory. For many years time-frequency analysis has been pursued mainly in engineering, but recently - with the development of wavelet theory - it has emerged as a thriving field of applied mathematics." "This book presents the first systematic introduction to time-frequency analysis understood as a central area of applied harmonic analysis, while at the same time honoring its interdisciplinary origins. Important principles are (a) classical Fourier analysis as a tool that is central in modern mathematics, (b) the mathematical structures based on the operations of translation and modulations (i.e., the Heisenberg group), (c) the many forms of the uncertainty principle, and (d) the omnipresence of Gaussian functions, both in the methodology of proofs and in important statements."--BOOK JACKET.

Genres: Mathematics

Paperback

First published December 15, 2000