03392nam 2200661 450 991082865050332120170822144258.01-4704-0498-2(CKB)3360000000465076(EBL)3114227(SSID)ssj0000888822(PQKBManifestationID)11453145(PQKBTitleCode)TC0000888822(PQKBWorkID)10865492(PQKB)11193317(MiAaPQ)EBC3114227(RPAM)15004282(PPN)19541781X(EXLCZ)99336000000046507620070912h20082008 uy| 0engur|n|---|||||txtccrClassical function theory, operator dilation theory, and machine computation on multiply-connected domains /Jim Agler, John Harland, Benjamin J. RaphaelProvidence, Rhode Island :American Mathematical Society,[2008]©20081 online resource (176 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 892"Volume 191, number 892 (second of 5 numbers)."0-8218-4046-0 Includes bibliographical references (pages 157-159).""Contents""; ""Preface""; ""Chapter 1. Generalizations of the Herglotz Representation Theorem, von Neumann's Inequality and the Sz.-Nagy Dilation Theorem to Multiply Connected Domains""; ""1.1. Introduction""; ""1.2. Preliminaries""; ""1.3. The First Herglotz Representation""; ""1.4. The Second Herglotz Representation""; ""1.5. The Third Herglotz Representation""; ""1.6. The Herglotz Representations and Operator Theory""; ""1.7. An Application""; ""Chapter 2. The Computational Generation of Counterexamples to the Rational Dilation Conjecture""; ""2.1. Introduction""""2.2. Mathematical Preliminaries""""2.3. Analysis of the Dilation Condition for Nonsingularly Hyperextremal Grammians""; ""2.4. Analysis of Dilation Extremal Grammians""; ""2.5. Algorithms""; ""2.6. A Computational Counterexample""; ""2.7. Plausibility Arguments""; ""Chapter 3. Arbitrary Precision Computations of the Poisson Kernel and Herglotz Kernels on Multiply-Connected Circle Domains""; ""3.1. Introduction""; ""3.2. Computation of the Functions""; ""3.3. Results""; ""Chapter 4. Schwartz Kernels on Multiply Connected Domains""; ""Appendix A. Convergence Results""""Appendix B. Example Inner Product Computation""""Bibliography""Memoirs of the American Mathematical Society ;no. 892.Geometric function theoryOperator theoryDilation theory (Operator theory)Functional analysisAnalytic functionsGeometric function theory.Operator theory.Dilation theory (Operator theory)Functional analysis.Analytic functions.515/.7Agler Jim66830Harland John1959-Raphael Benjamin J.1974-MiAaPQMiAaPQMiAaPQBOOK9910828650503321Classical function theory, operator dilation theory, and machine computation on multiply-connected domains3958932UNINA