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

Author: Jim Agler; John Harland; Benjamin J Raphael
Publisher: Providence, R.I. : American Mathematical Society, ©2008.
Series: Memoirs of the American Mathematical Society, no. 892.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

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  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jim Agler; John Harland; Benjamin J Raphael
ISBN: 9780821840467 0821840460
OCLC Number: 173368759
Notes: "Volume 191, number 892 (second of 5 numbers)."
Description: vii, 159 pages : illustrations ; 26 cm.
Contents: Generalizations of the Herglotz representation theorem, von Neumann's inequality and the Sz.-Nagy Dilation theorem to multiply connected domains --
Preliminaries --
The first Herglotz representation --
The second Herglotz representation --
The third Herglotz representation --
The Herglotz representations and operator theory --
An application --
The Computational generation of counterexamples to the rational dilation conjecture --
Mathematical preliminaries --
Analysis of the dilation condition for nonsingularly hyperextremal Grammians --
Analysis of dilation extremal grammians --
Algorithms --
A computational counterexample --
Plausibility arguments --
Arbitrary precision computations of the poisson kernel and Herglotz kernels on multiply-connected circle domains --
Computation of the functions --
Results --
Schwartz Kernels on multiply connected domains.
Series Title: Memoirs of the American Mathematical Society, no. 892.
Responsibility: Jim Agler, John Harland, Benjamin J. Raphael.
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