Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators
Seiten
1998
American Mathematical Society (Verlag)
9780821810804 (ISBN)
American Mathematical Society (Verlag)
9780821810804 (ISBN)
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Presents a fresh conceptual framework, leading to an effective structured method, for analyzing and classifying self-adjoint boundary conditions. This title offers detailed treatment in the literature of the two topics: complex symplectic spaces - their geometry and linear algebra - and quasi-differential operators.
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.
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.
Introduction: Fundamental algebraic and geometric concepts applied to the theory of self-adjoint boundary value problems Maximal and minimal operators for quasi-differential expressions, and GKN-theory Symplectic geometry and boundary value problems Regular boundary value problems Singular boundary value problems Appendix A. Constructions for quasi-differential operators Appendix B. Complexification of real symplectic spaces, and the real GKN-theorem for real operators References.
| Erscheint lt. Verlag | 30.10.1998 |
|---|---|
| Reihe/Serie | Mathematical Surveys and Monographs |
| Verlagsort | Providence |
| Sprache | englisch |
| Gewicht | 567 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-13 | 9780821810804 / 9780821810804 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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