Karlheinz Gröchenig Knihy

The book systematically explores the foundations of time-frequency analysis, a modern branch of harmonic analysis that examines functions and operators through translations and modulations. It covers essential topics such as the short-time Fourier transform, Wigner distribution, Gabor frames, and pseudodifferential operators. While motivated by applications in signal analysis and quantum mechanics, the focus remains on the mathematical structures of time-frequency analysis, tracing its origins to early quantum mechanics developments in the 1930s.

This book collects the proceedings of the 2012 Abel Symposium, held at the Norwegian Academy of Science and Letters, Oslo. The Symposium, and this book, are focused on two important fields of modern mathematical analysis: operator-related function theory and time-frequency analysis; and the profound interplay between them. Among the original contributions and overview lectures gathered here are a paper presenting multifractal analysis as a bridge between geometric measure theory and signal processing; local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions; Bernstein's problem on weighted polynomial approximation; singular distributions and symmetry of the spectrum; and many others. Offering a selection of the latest and most exciting results obtained by world-leading researchers, the book will benefit scientists working in Harmonic and Complex Analysis, Mathematical Physics and Signal Processing.