Toeplitz approach to problems of the uncertainty principle

Author(s)

• Poltoratski, Alexei

Bibliographic Information

Toeplitz approach to problems of the uncertainty principle

Alexei Poltoratski

（Regional conference series in mathematics, no. 121）

Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, c2015

• : pbk

Note

"NSF-CBMS Regional Conference in the Mathematical Sciences : Uncertainty Principles in Harmonic Analysis : Gap and Type Problems, held at Clemson University, Clemson, South Carolina, August 12-16, 2013."--T.p. verso

Bibliography: p. 211-216

Description and Table of Contents

Description

The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems. These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Polya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts.

Table of Contents

Mathematical shapes of uncertainty Gap theorems A problem by Polya and Levinson Determinacy of measures and oscillations of high-pass signals Beurling-Malliavin and Bernstein's problems The type problem Toeplitz approach to UP Toeplitz version of the Beurling-Malliavin theory Bibliography

by "Nielsen BookData"

Details

• NCID: BB18282537
• ISBN:
  • 9781470420178
• LCCN: 2014043343
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: vii, 216 p.
• Size: 26 cm
• Classification:
  • LCC : QC174.17.H4
  • DC23 : 530.12
• Subject Headings:
  • LCSH : Heisenberg uncertainty principle -- Congresses
  • LCSH : Functional analysis -- Congresses
  • LCSH : Toeplitz, Otto, 1881-1940
  • FREE : Functions of a complex variable. msc
  • FREE : Special functions (33-XX deals with the properties of functions as functions). msc
  • FREE : Ordinary differential equations. msc
  • FREE : Harmonic analysis on Euclidean spaces. msc
• Parent Bibliography ID:
  • BA0000944X