Hardcover ISBN:  9780821810804 
Product Code:  SURV/61 
187 pp 
List Price:  $67.00 
MAA Member Price:  $60.30 
AMS Member Price:  $53.60 
Electronic ISBN:  9781470412883 
Product Code:  SURV/61.E 
187 pp 
List Price:  $63.00 
MAA Member Price:  $56.70 
AMS Member Price:  $50.40 

Book DetailsMathematical Surveys and MonographsVolume: 61; 1999MSC: Primary 34; 58; Secondary 11; 47;
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 spaces—their geometry and linear algebra—and 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.
ReadershipResearch 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.

Table of Contents

Chapters

I. Introduction: Fundamental algebraic and geometric concepts applied to the theory of selfadjoint boundary value problems

II. Maximal and minimal operators for quasidifferential expressions, and GKNtheory

III. Symplectic geometry and boundary value problems

IV. Regular boundary value problems

V. Singular boundary value problems


Additional Material

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


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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 spaces—their geometry and linear algebra—and 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.
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.

Chapters

I. Introduction: Fundamental algebraic and geometric concepts applied to the theory of selfadjoint boundary value problems

II. Maximal and minimal operators for quasidifferential expressions, and GKNtheory

III. Symplectic geometry and boundary value problems

IV. Regular boundary value problems

V. Singular boundary value problems

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