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Lecture Notes in Mathematics

Hyponormal Quantization of Planar Domains

Exponential Transform in Dimension Two

Authors: Gustafsson, Björn, Putinar, Mihai

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  • A self-contained exposition of the concept of "mother body" in potential theory
  • Intriguing numerical experiments lacking theoretical explanation
  • A new class of complex polynomials orthogonal with respect to a non Lebesgue space type norm
  • Optimal storage and exact reconstruction of moments of a class of planar algebraic domains
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eBook 28,88 €
price for Spain (gross)
  • ISBN 978-3-319-65810-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-65809-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

This book exploits the classification of a class of linear bounded operators with rank-one self-commutators in terms of their spectral parameter, known as the principal function. The resulting dictionary between two dimensional planar shapes with a degree of shade and Hilbert space operators turns out to be illuminating and beneficial for both sides. An exponential transform, essentially a Riesz potential at critical exponent, is at the heart of this novel framework; its best rational approximants unveil a new class of complex orthogonal polynomials whose asymptotic distribution of zeros is thoroughly studied in the text. Connections with areas of potential theory, approximation theory in the complex domain and fluid mechanics are established.

The text is addressed, with specific aims, at experts and beginners in a wide range of areas of current interest: potential theory, numerical linear algebra, operator theory, inverse problems, image and signal processing, approximation theory, mathematical physics.

Table of contents (8 chapters)

Table of contents (8 chapters)
  • Introduction

    Pages 1-5

    Gustafsson, Björn (et al.)

  • The Exponential Transform

    Pages 7-21

    Gustafsson, Björn (et al.)

  • Hilbert Space Factorization

    Pages 23-45

    Gustafsson, Björn (et al.)

  • Exponential Orthogonal Polynomials

    Pages 47-56

    Gustafsson, Björn (et al.)

  • Finite Central Truncations of Linear Operators

    Pages 57-75

    Gustafsson, Björn (et al.)

Buy this book

eBook 28,88 €
price for Spain (gross)
  • ISBN 978-3-319-65810-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 36,39 €
price for Spain (gross)
  • ISBN 978-3-319-65809-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Hyponormal Quantization of Planar Domains
Book Subtitle
Exponential Transform in Dimension Two
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2199
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-65810-0
DOI
10.1007/978-3-319-65810-0
Softcover ISBN
978-3-319-65809-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 150
Number of Illustrations
16 illustrations in colour
Topics