Interpolation Theory and Its Applications

Lev A. Sakhnovich

ISBN 10: 0792348303 / ISBN 13: 9780792348306

Verlag: Springer Netherlands, Springer Netherlands Nov 1997, 1997

Beschreibung

This item is printed on demand - Print on Demand Titel. Neuware -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. 220 pp. Englisch.

Bestandsnummer des Verkäufers 9780792348306

Bibliografische Details

• Titel: Interpolation Theory and Its Applications
• Verlag: Springer Netherlands, Springer Netherlands Nov 1997
• Erscheinungsjahr: 1997
• Sprache: Englisch
• ISBN-10: 0792348303
• ISBN-13: 9780792348306
• Einband: Buch
• Zustand: Neu

Über diesen Titel

Inhaltsangabe

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.