Hyponormal Quantization of Planar Domains

Exponential Transform in Dimension Two

  • Björn Gustafsson
  • Mihai Putinar

Part of the Lecture Notes in Mathematics book series (LNM, volume 2199)

Table of contents

  1. Front Matter
    Pages i-x
  2. Björn Gustafsson, Mihai Putinar
    Pages 1-5
  3. Björn Gustafsson, Mihai Putinar
    Pages 7-21
  4. Björn Gustafsson, Mihai Putinar
    Pages 23-45
  5. Björn Gustafsson, Mihai Putinar
    Pages 47-56
  6. Björn Gustafsson, Mihai Putinar
    Pages 57-75
  7. Björn Gustafsson, Mihai Putinar
    Pages 77-92
  8. Björn Gustafsson, Mihai Putinar
    Pages 93-117
  9. Björn Gustafsson, Mihai Putinar
    Pages 119-124
  10. Back Matter
    Pages 125-150

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.


momentum problem exponential transform orthogonal polynomial hyponormal operator rational approximation

Authors and affiliations

  • Björn Gustafsson
    • 1
  • Mihai Putinar
    • 2
  1. 1.Department of MathematicsKTH Royal Institute of TechnologyStockholmSweden
  2. 2.Mathematics DepartmentUniversity of CaliforniaSanta BarbaraUSA

Bibliographic information