Vladimir A. Kondratiev's Books

On Spectral Theory of Elliptic Operators

By: Yuri V. Egorov,Vladimir A. Kondratiev

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On Spectral Theory of Elliptic Operators

By: Yuri V. Egorov,Vladimir A. Kondratiev

It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results.

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Page Count

336

Publisher

Birkhäuser

Published Date

ISBN 10

303489029X

ISBN 13

9783034890298

On Spectral Theory of Elliptic Operators

By: Youri Egorov,Vladimir A. Kondratiev

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On Spectral Theory of Elliptic Operators

By: Youri Egorov,Vladimir A. Kondratiev

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Page Count

194

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3764353902

ISBN 13

9783764353902

Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

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Differentiable Measures and the Malliavin Calculus

By: Vladimir Igorevich Bogachev

This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.

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Page Count

506

Publisher

American Mathematical Soc.

Published Date

ISBN 10

082184993X

ISBN 13

9780821849934

Book's by Vladimir A. Kondratiev

On Spectral Theory of Elliptic Operators

On Spectral Theory of Elliptic Operators

On Spectral Theory of Elliptic Operators

On Spectral Theory of Elliptic Operators

Differentiable Measures and the Malliavin Calculus

Differentiable Measures and the Malliavin Calculus

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