Canonical Complex Integral Operators

  • Steven G. Krantz
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

In the function theory of one complex variable the obvious “canonical” integral kernels are the Cauchy kernel and the Poisson kernel. The Cauchy kernelmay be discovered naturally by way of power series considerations, or partial differential equations considerations, or conformality considerations. The Poisson kernel is the real part of the Cauchy kernel. It also arises naturally as the solution operator for the Dirichlet problem. It is rather more difficult to get one’s hands on integral reproducing kernels in several complex variables.


Asymptotic Expansion Holomorphic Function Complex Variable Bergman Space Pseudoconvex Domain 
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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Dept. MathematicsWashington UniversitySt.LouisUSA

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