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Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasidifferential Operators (Mathematical Surveys ,Used
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In the classical theory of selfadjoint 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 skewsymmetric 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 selfadjoint 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 spacestheir geometry and linear algebraand quasidifferential operators. Features: Authoritative and systematic exposition of the classical theory for selfadjoint 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 quasidifferential operators, offering the only extensive treatment of these topics in book form. New conceptual and structured methods for selfadjoint boundary value problems. Extensive and exhaustive tabulations of all existing kinds of selfadjoint boundary conditions for regular and for singular ordinary quasidifferential operators of all orders up through six.
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