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Interpolation Theory and Its Applications (Hardcover, 1997 ed.)
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Interpolation Theory and Its Applications (Hardcover, 1997 ed.)
Series: Mathematics and Its Applications, 428
Expected to ship within 10 - 15 working days
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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.
General
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