Classical function theory, operator dilation theory, and machine computation on multiply-connected domains
Author(s)
Bibliographic Information
Classical function theory, operator dilation theory, and machine computation on multiply-connected domains
（Memoirs of the American Mathematical Society, no. 892）
American Mathematical Society, 2008
Available at / 14 libraries
-
No Libraries matched.
- Remove all filters.
Note
Includes bibliographical references (p. 157-159)
"Volume 191, number 892 (second of 5 numbers)." -- T.p
Description and Table of Contents
Description
This work begins with the presentation of generalizations of the classical Herglotz Representation Theorem for holomorphic functions with positive real part on the unit disc to functions with positive real part defined on multiply-connected domains. The generalized Herglotz kernels that appear in these representation theorems are then exploited to evolve new conditions for spectral set and rational dilation conditions over multiply-connected domains. These conditions form the basis for the theoretical development of a computational procedure for probing a well-known unsolved problem in operator theory, the so called rational dilation conjecture. Arbitrary precision algorithms for computing the Herglotz kernels on circled domains are presented and analyzed. These algorithms permit an effective implementation of the computational procedure which results in a machine generated counterexample to the rational dilation conjecture.
Table of Contents
Generalizations of the Herglotz representation theorem, von Neumann's inequality and the Sz.-Nagy dilation theorem to multiply connected domains The computational generation of counterexamples to the rational dilation conjecture Arbitrary precision computations of the Poisson kernel and Herglotz kernels on multiply-connected circle domains Schwartz kernels on multiply connected domains Appendix A. Convergence results Appendix B. Example inner product computation Bibliography.
by "Nielsen BookData"