Complete Second Order Linear Differential Equations in Hilbert Spaces

By:

Alexander Ya Shklyar

Format:

Hardback

Series:

Operator Theory: Advances and Applications

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Description

Hilbert spaces are Banach spaces where the norm is induced by the inner product. Incomplete second order differential equations and first order equations in Banach spaces are a classical part of functional analysis. This text attempts to present a unified systematic theory of second order differential equations (y"(t)+By'(t)+Cy(t)=0), including the well-posedness of the Cauchy, Dirichlet and Neumann problems; boundary conditions ensuring solvability of boundary-value problems; boundary behaviour and the extension of solutions on a finite interval; stabilization and stability of solutions at infinity; and boundary-value problems on a semi-line. The theory is developed in a special but important case, which can be considered as a model. Exhaustive answers to all the posed questions are given, with special emphasis on the effects arising for complete second order equations which do not arise for incomplete second order or first order equations. To achieve this, new results in the spectral theory of pairs of operators and the boundary behaviour of integral transformations have been developed.

Release date Australia

February 18th, 1997

Author

Alexander Ya Shklyar

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational
Undergraduate

Illustrations

XII, 220 p.

Pages

220

Series

Operator Theory: Advances and Applications

Dimensions

156x234x14

ISBN-13

9783764353773

Product ID

2856142

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Complete Second Order Linear Differential Equations in Hilbert Spaces

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