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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.

Mathematics. --- Dynamical Systems and Ergodic Theory. --- Fourier Analysis. --- Partial Differential Equations. --- Approximations and Expansions. --- Image Processing and Computer Vision. --- Signal, Image and Speech Processing. --- Computer vision. --- Differentiable dynamical systems. --- Fourier analysis. --- Differential equations, partial. --- Mathématiques --- Vision par ordinateur --- Dynamique différentiable --- Analyse de Fourier --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Adaptive control systems. --- Self-adaptive control systems --- Image processing. --- Approximation theory. --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Artificial intelligence --- Feedback control systems --- Self-organizing systems --- Machine vision --- Vision, Computer --- Image processing --- Pattern recognition systems --- Math --- Science --- Partial differential equations --- Analysis, Fourier --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Optical data processing. --- Signal processing. --- Speech processing systems. --- Computational linguistics --- Electronic systems --- Information theory --- Modulation theory --- Oral communication --- Speech --- Telecommunication --- Singing voice synthesizers --- Pictorial data processing --- Picture processing --- Processing, Image --- Imaging systems --- Optical data processing --- Processing, Signal --- Information measurement --- Signal theory (Telecommunication) --- Optical computing --- Visual data processing --- Bionics --- Electronic data processing --- Integrated optics --- Photonics --- Computers --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Optical equipment

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Mathematics