Canonical Complex Integral Operators
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.
KeywordsAsymptotic Expansion Holomorphic Function Complex Variable Bergman Space Pseudoconvex Domain
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