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.

1 P. Abry, S. Jaffard, and H. Wendt: A bridge between geometric measure theory and signal processing: Multifractal analysis.- 2 D. Batenkov and Y. Yomdin: Local and global geometry of Prony systems and Fourier reconstruction of piecewise-smooth functions.- 3 H. Feichtinger: Elements of postmodern harmonic analysis.- 4 G. Kozma and A. Olevskii: Singular distributions and symmetry of the spectrum.- 5 I. Laba: Recent progress on Favard length estimates for planar Cantor sets.- 6 A. Poltoratski: Bernstein's problem on weighted polynomial approximation.- 7 J. Sjöstrand: Return to equilibrium, non-self-adjointness and symmetries, recent results with M. Hitrik and F. Hérau.- 8 S. Treil: A remark on two weight estimates for positive dyadic operators.