Harmonic Analysis and Applications

ISBN-13: 9783030618865 / Angielski / Twarda / 2021 / 359 str.

Michael Th Rassias

Recenzje

"It might serve as the foundation for the occasional graduate topics course in harmonic analysis. Many of the contributed chapters present new results and most provide a thoughtful introduction along with sufficient references to orient readers unfamiliar with the relevant subfield." (Brody Johnson, MAA Reviews, October 3, 2021)

Spis treści

Sampling and Approximation in Shift Invariant subspaces of L2(ℝ) (Atreas).- Optimal ℓ¹ rank one matrix decomposition (Balan).- An arithmetical function related to Báez-Duarte’s criterion for the Riemann hypothesis (Balazard).- Large Sets Avoiding Rough Patterns (Zahl).- PDE methods in Random Matrix Theory (Hall).- Structure and optimisation in computational harmonic analysis –  On key aspects in sparse regularisation (Hansen).- Reflections on a Theorem of Boas and Pollard (Heil).- The Andoni-Krauthgamer-Razenshteyn characterization of sketchable norms fails for sketchable metrics (Noar).- Degree of convergence of some operators ^ 1 (Mohapatra).- Real variable methods in harmonic analysis and Navier–Stokes equations (Lemarié-Rieusset).- Explore intrinsic geometry of sleep dynamics and predict sleep stage by unsupervised learning techniques (Wu).- Harmonic functions in slabs and half-spaces (Madych).

O autorze

​Michael Th. Rassias is a Research Fellow at the University of Zürich, a visiting researcher at the Institute for Advanced Study, Princeton, as well as a visiting Associate Professor at the Moscow Institute of Physics and Technology. He obtained his PhD in Mathematics from ETH-Zürich in 2014. During the academic year 2014-2015, he was a Postdoctoral researcher at the Department of Mathematics of Princeton University and the Department of Mathematics of ETH-Zürich, conducting research at Princeton. While at Princeton, he prepared with John F. Nash, Jr. the volume "Open Problems in Mathematics", Springer, 2016. He has received several awards in mathematical problem-solving competitions, including a Silver medal at the International Mathematical Olympiad of 2003 in Tokyo. He has authored and edited several books with Springer. His current research interests lie in mathematical analysis, analytic number theory, and more specifically the Riemann Hypothesis, Goldbach’s conjecture, the distribution of prime numbers, approximation theory, functional equations and analytic inequalities.

Blurb

This edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as structure and optimization in computational harmonic analysis, sampling and approximation in shift invariant subspaces of L2(ℝ), optimal rank one matrix decomposition, the Riemann Hypothesis, large sets avoiding rough patterns, Hardy Littlewood series, Navier–Stokes equations, sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools, harmonic functions in slabs and half-spaces, Andoni –Krauthgamer –Razenshteyn characterization of sketchable norms fails for sketchable metrics, random matrix theory, multiplicative completion of redundant systems in Hilbert and Banach function spaces.

Efforts have been made to ensure that the content of the book constitutes a valuable resource for graduate students as well as senior researchers working on Harmonic Analysis and its various interconnections with related areas.