Mathematical Surveys and Monographs 1999; 187 pp; hardcover Volume: 61 ISBN10: 0821810804 ISBN13: 9780821810804 List Price: US$60 Member Price: US$48 Order Code: SURV/61
 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.
Readership Research mathematicians and graduate students interested in boundary value problems represented by selfadjoint differential operators, and symplectic linear algebra and geometry for real and complex vector spaces, with applications; mathematical physicists and engineers. Reviews "With this monograph Everitt and Markus have produced a major advance in our understanding of the structure of selfadjoint boundary conditions for regular and singular linear ordinary differential equations of arbitrary order \(n\) and with arbitrary deficiency index \(d\)."  Mathematical Reviews, Featured Review Table of Contents  Introduction: Fundamental algebraic and geometric concepts applied to the theory of selfadjoint boundary value problems
 Maximal and minimal operators for quasidifferential expressions, and GKNtheory
 Symplectic geometry and boundary value problems
 Regular boundary value problems
 Singular boundary value problems
 Appendix A. Constructions for quasidifferential operators
 Appendix B. Complexification of real symplectic spaces, and the real GKNtheorem for real operators
 References
