Agler J. Classical function theory, operator dilation theory, and machine computation on multiply-connected domains / Agler J., Harland J., Raphael B.J. - Providence: AMS, 2008. - 159 p. - (Memoirs of the American mathematical society; N 892). - ISSN 0065-9266; ISBN 0821840460  Место хранения:   013 | Институт математики СО РАН | Новосибирск | Библиотека

Оглавление / Contents

Preface ....................................................... vii Chapter 1. Generalizations of the Herglotz Representation Theorem, von Neumann's Inequality and the Sz.-Nagy Dilation Theorem to Multiply Connected Domains ....... 1 1.1. Introduction .................................... 1 1.2. Preliminaries ................................... 7 1.3. The First Herglotz Representation .............. 12 1.4. The Second Herglotz Representation ............. 21 1.5. The Third Herglotz Representation .............. 23 1.6. The Herglotz Representations and Operator Theory ......................................... 28 1.7. An Application ................................. 33 Chapter 2. The Computational Generation of Counterexamples to the Rational Dilation Conjecture .................... 61 2.1. Introduction ................................... 61 2.2. Mathematical Preliminaries ..................... 64 2.3. Analysis of the Dilation Condition for Nonsingularly Hyperextremal Grammians .......... 72 2.4. Analysis of Dilation Extremal Grammians ........ 82 2.5. Algorithms ..................................... 89 2.6. A Computational Counterexample ................ 100 2.7. Plausibility Arguments ........................ 105 Chapter 3. Arbitrary Precision Computations of the Poisson Kernel and Herglotz Kernels on Multiply-Connected Circle Domains ..................................... 109 3.1. Introduction .................................. 109 3.2. Computation of the Functions .................. 112 3.3. Results ....................................... 119 Chapter 4. Schwartz Kernels on Multiply Connected Domains ..... 127 Appendix A. Convergence Results ............................... 139 Appendix B. Example Inner Product Computation ................. 155 Bibliography .................................................. 157