© 2005

Quadrature Domains and Their Applications

The Harold S. Shapiro Anniversary Volume

  • Peter Ebenfelt
  • Björn Gustafsson
  • Dmitry Khavinson
  • Mihai Putinar


  • Contains both original articles and survey papers covering quite a wide scope of ideas and applications in potential theory, complex analysis and applications

  • Expanded version of talks and contributed papers presented at the conference in March of 2003 at the UCSB to celebrate the 75th birthday of Harold S. Shapiro

  • Survey articles, written by the leading experts in the field, will help to orient the beginners in the vastly increasing literature on the subject

Conference proceedings

Part of the Operator Theory: Advances and Applications book series (OT, volume 156)

Table of contents

  1. Front Matter
    Pages i-xxviii
  2. Björn Gustafsson, Harold S. Shapiro
    Pages 1-25
  3. Alexandru Aleman, Håakan Hedenmalm, Stefan Richter
    Pages 27-59
  4. Joseph A. Cima, Alec Matheson, William T. Ross
    Pages 79-111
  5. Darren Crowdy
    Pages 113-129
  6. Peter Dure, Alexander Schuste, Dragan Vukotić
    Pages 131-150
  7. P. Ebenfelt, D. Khavinson, H.S. Shapiro
    Pages 151-172
  8. Björn Gustafsson, Mihai Putinar
    Pages 173-194

About these proceedings


Quadrature domains were singled out about 30 years ago by D. Aharonov and H.S. Shapiro in connection with an extremal problem in function theory. Since then, a series of coincidental discoveries put this class of planar domains at the center of crossroads of several quite independent mathematical theories, e.g., potential theory, Riemann surfaces, inverse problems, holomorphic partial differential equations, fluid mechanics, operator theory. The volume is devoted to recent advances in the theory of quadrature domains, illustrating well the multi-facet aspects of their nature. The book contains a large collection of open problems pertaining to the general theme of quadrature domains.


Operatortheorie Potential Spektraltheorie calculus differential equation extrema numerische Analysis operator theory orthogonale Polynome subharmonic function

Editors and affiliations

  • Peter Ebenfelt
    • 1
  • Björn Gustafsson
    • 2
  • Dmitry Khavinson
    • 3
  • Mihai Putinar
    • 4
  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of MathematicsRoyal Institute of Technology (KTH)StockholmSweden
  3. 3.Department of Mathematical SciencesUniversity of ArkansasFayettevilleUSA
  4. 4.Mathematics DepartmentUniversity of California, Santa BarbaraSanta BarbaraUSA

Bibliographic information

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