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Classical function theory, operator dilation theory, and machine computation on multiply-connected domains

About this Title

Jim Agler, John Harland and Benjamin J. Raphael

Publication: Memoirs of the American Mathematical Society
Publication Year: 2008; Volume 191, Number 892
ISBNs: 978-0-8218-4046-7 (print); 978-1-4704-0498-7 (online)
MathSciNet review: 2375060
MSC: Primary 47A20; Secondary 30-02, 30-04, 30E20, 46E15, 47-02

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Table of Contents


  • 1. Generalizations of the Herglotz representation theorem, von Neumann’s inequality and the Sz.-Nagy dilation theorem to multiply connected domains
  • 2. The computational generation of counterexamples to the rational dilation conjecture
  • 3. Arbitrary precision computations of the Poisson Kernel and Herglotz Kernels on multiply-connected circle domains
  • 4. Schwartz kernels on multiply connected domains