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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
Front Cover for Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators
Available Formats:
Hardcover ISBN: 978-0-8218-1080-4
Product Code: SURV/61
187 pp 
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
187 pp 
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
Front Cover for Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators
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  • Front Cover for Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators
  • Back Cover for Boundary Value Problems and Symplectic Algebra for Ordinary Differential and Quasi-differential Operators
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
187 pp 
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
187 pp 
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
    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.

    Readership

    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.

  • Table of Contents
     
     
    • 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
  • Additional Material
     
     
  • 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
  • Request Review Copy
  • Get Permissions
Volume: 611999
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.

Readership

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
  • 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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