Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators
著者
書誌事項
Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators
(Mathematical surveys and monographs, v. 61)
American Mathematical Society, c1999
大学図書館所蔵 件 / 全52件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. 179-180) and indexes
内容説明・目次
内容説明
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.
目次
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.
「Nielsen BookData」 より