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Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators

Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators (Hardback)

£56.50
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Synopsis

In the classical theory of self-adjoint boundary value problems for linear ordinary differential operators there is a fundamental, but rather mysterious, interplay between the symmetric (conjugate) bilinear scalar product of the basic Hilbert space and the skew-symmetric boundary form of the associated differential expression. This book presents a new conceptual framework, leading to an effective structured method, for analyzing and classifying all such self-adjoint boundary conditions. The program is carried out by introducing innovative new mathematical structures which relate the Hilbert space to a complex symplectic space.This work offers the first systematic detailed treatment in the literature of these two topics: complex symplectic spaces - their geometry and linear algebra - and quasi-differential operators. This title features: authoritative and systematic exposition of the classical theory for self-adjoint linear ordinary differential operators (including a review of all relevant topics in texts of Naimark, and Dunford and Schwartz); introduction and development of new methods of complex symplectic linear algebra and geometry and of quasi-differential operators, offering the only extensive treatment of these topics in book form; new conceptual and structured methods for self-adjoint boundary value problems; and, extensive and exhaustive tabulations of all existing kinds of self-adjoint boundary conditions for regular and for singular ordinary quasi-differential operators of all orders up through six.

Science & MathematicsMathematicsAlgebraScience & MathematicsMathematicsCalculus & mathematical analysisDifferential calculus & equationsScience & MathematicsMathematicsGeometry Publisher: American Mathematical Society Publication Date: 01/01/1998 ISBN-13: 9780821810804  Details: Type: Hardback Format: Books
Availability: To Order. Estimated despatch in 1-3 weeks.  

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