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Mathematical Surveys and Monographs
1999; 187 pp; hardcover
List Price: US$60
Member Price: US$48
Order Code: SURV/61
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.
Research mathematicians and graduate students interested in boundary value problems represented by self-adjoint differential operators, and symplectic linear algebra and geometry for real and complex vector spaces, with applications; mathematical physicists and engineers.
"With this monograph Everitt and Markus have produced a major advance in our understanding of the structure of self-adjoint boundary conditions for regular and singular linear ordinary differential equations of arbitrary order \(n\) and with arbitrary deficiency index \(d\)."
-- Mathematical Reviews, Featured Review
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