Foundations of Time-Frequency Analysis

"Foundations of Time-Frequency Analysis provides a clear and thorough exposition of some of the fundamental results in the theory and gives some important perspectives on a rapidly growing field . . . An important feature of the book is complete, detailed proofs of all claims and extensive motivation of topics . . . The author has chosen topics that illuminate a path toward some of the most interesting and challenging research areas in mathematical time-frequency analysis. A graduate student or researcher seeking research problems in this area can come to no better source . . . The book is definitely suitable for a graduate-level course in mathematical time-frequency analysis. It assumes a background in real analysis, Fourier analysis and Hilbert spaces. It is also suitable for self-study, as the exposition is superb."   ―Mathematical Reviews

"This book is written by one of the leading experts in Gabor analysis and deserves considerable interest. It gives a unified approach to most of the modern theory for time-frequency analysis from a mathematician's point of view, with new proofs of many recent results."   ―Zentralblatt Math

"In contrast with the crowded market for wavelet expositions, this book has no up-to-date competitors in its niche, the rigorous mathematical theory. Groechenig makes contact with representation theory, operator algebra theory, and concludes with applications to pseudodifferential operators. But elsewhere he develops inequalities with implications for numerical analysis that should interest signal-processing engineers. He also explains how foundational investigations of quantum theory provided the subject with some of its original impetus.... Throughout, the author displays generosity to his readers as well as fastidious attention to mathematical detail. Of potential interest to graduate students and faculty in mathematics, physics, electrical engineering, and computer science."   ―Choice