Interpolation Theory and Its Applications: 428 (Mathematics and Its Applications, 428) - Hardcover

Sakhnovich, Lev A.

Hardcover

ISBN 10: 0792348303 ISBN 13: 9780792348306

Publisher: Springer, 1997

Synopsis

1. Interpolation problems play an important role both in theoretical and applied investigations. This explains the great number of works dedicated to classical and new interpolation problems ([1)-[5], [8), [13)-[16], [26)-[30], [57]). In this book we use a method of operator identities for investigating interpo­ lation problems. Following the method of operator identities we formulate a general interpolation problem containing the classical interpolation problems (Nevanlinna­ Pick, Caratheodory, Schur, Humburger, Krein) as particular cases. We write down the abstract form of the Potapov inequality. By solving this inequality we give the description of the set of solutions of the general interpolation problem in the terms of the linear-fractional transformation. Then we apply the obtained general results to a number of classical and new interpolation problems. Some chapters of the book are dedicated to the application of the interpola­ tion theory results to several other problems (the extension problem, generalized stationary processes, spectral theory, nonlinear integrable equations, functions with operator arguments). 2. Now we shall proceed to a more detailed description of the book contents.

About this title

Synopsis

This volume is devoted to the use of the method of operator identities for investigating interpolation and expansion problems. A general interpolation problem comprising both classical and new elements is formulated. The solution of an abstract form of the Potapov inequality enables the description of the set of solutions of the general interpolation problem. Connections between the solved interpolation problem and important problems of analysis occurring in, for example, spectral theory, nonlinear integrable equations, and generalized stationary processes, are then considered. This book should be of interest to graduate students and researchers whose work involves approximations and expansions; operator theory; measure and integration; general mathematics systems; and Fourier analysis.

Edition details

• Publisher: Springer
• Publication date: 1997
• Language: English
• ISBN 10: 0792348303
• ISBN 13: 9780792348306
• Binding: Hardcover
• Number of pages: 215