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Toeplitz Approach to Problems of the Uncertainty Principle

Alexei Poltoratski Texas A&M University, College Station, TX
A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-1-4704-2017-8
Product Code: CBMS/121
List Price: $52.00 MAA Member Price:$46.80
AMS Member Price: $41.60 Electronic ISBN: 978-1-4704-2262-2 Product Code: CBMS/121.E List Price:$49.00
MAA Member Price: $44.10 AMS Member Price:$39.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $78.00 MAA Member Price:$70.20
AMS Member Price: $62.40 Click above image for expanded view Toeplitz Approach to Problems of the Uncertainty Principle Alexei Poltoratski Texas A&M University, College Station, TX A co-publication of the AMS and CBMS Available Formats:  Softcover ISBN: 978-1-4704-2017-8 Product Code: CBMS/121  List Price:$52.00 MAA Member Price: $46.80 AMS Member Price:$41.60
 Electronic ISBN: 978-1-4704-2262-2 Product Code: CBMS/121.E
 List Price: $49.00 MAA Member Price:$44.10 AMS Member Price: $39.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$78.00 MAA Member Price: $70.20 AMS Member Price:$62.40
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1212015; 216 pp
MSC: Primary 30; 33; 34; 42;

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 Pólya 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.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in harmonic and complex analysis and special problems.

• Chapters
• 1. Mathematical shapes of uncertainty
• 2. Gap theorems
• 3. A problem by Pólya and Levinson
• 4. Determinacy of measures and oscillations of high-pass signals
• 5. Beurling-Malliavin and Bernstein’s problems
• 6. The Type Problem
• 7. Toeplitz approach to UP
• 8. Toeplitz version of the Beurling-Malliavin theory

• Requests

Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
Volume: 1212015; 216 pp
MSC: Primary 30; 33; 34; 42;

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 Pólya 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.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in harmonic and complex analysis and special problems.

• Chapters
• 1. Mathematical shapes of uncertainty
• 2. Gap theorems
• 3. A problem by Pólya and Levinson
• 4. Determinacy of measures and oscillations of high-pass signals
• 5. Beurling-Malliavin and Bernstein’s problems
• 6. The Type Problem
• 7. Toeplitz approach to UP
• 8. Toeplitz version of the Beurling-Malliavin theory
Review Copy – for reviewers who would like to review an AMS book
Accessibility – to request an alternate format of an AMS title
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