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Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators

W. Norrie Everitt University of Birmingham, Birmingham, UK
Lawrence Markus University of Minnesota, Minneapolis, MN
Available Formats:
Hardcover ISBN: 978-0-8218-1080-4
Product Code: SURV/61
List Price: $67.00 MAA Member Price:$60.30
AMS Member Price: $53.60 Electronic ISBN: 978-1-4704-1288-3 Product Code: SURV/61.E List Price:$63.00
MAA Member Price: $56.70 AMS Member Price:$50.40
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List Price: $100.50 MAA Member Price:$90.45
AMS Member Price: $80.40 Click above image for expanded view Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators W. Norrie Everitt University of Birmingham, Birmingham, UK Lawrence Markus University of Minnesota, Minneapolis, MN Available Formats:  Hardcover ISBN: 978-0-8218-1080-4 Product Code: SURV/61  List Price:$67.00 MAA Member Price: $60.30 AMS Member Price:$53.60
 Electronic ISBN: 978-1-4704-1288-3 Product Code: SURV/61.E
 List Price: $63.00 MAA Member Price:$56.70 AMS Member Price: $50.40 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$100.50 MAA Member Price: $90.45 AMS Member Price:$80.40
• Book Details

Mathematical Surveys and Monographs
Volume: 611999; 187 pp
MSC: Primary 34; 58; Secondary 11; 47;

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.

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.
• 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.

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.

• Chapters
• I. Introduction: Fundamental algebraic and geometric concepts applied to the theory of self-adjoint boundary value problems
• II. Maximal and minimal operators for quasi-differential expressions, and GKN-theory
• III. Symplectic geometry and boundary value problems
• IV. Regular boundary value problems
• V. Singular boundary value problems

• Reviews

• 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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Volume: 611999; 187 pp
MSC: Primary 34; 58; Secondary 11; 47;

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.

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.
• 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.

• 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 $d$.