Boundary value problems and symplectic algebra for ordinary differential and quasi-differential operators / W. Norrie Everitt, Lawrence Markus.

Format:

Book

Author/Creator:

Everitt, W. N. (William Norrie), 1924-2011.

Contributor:

Markus, L. (Lawrence), 1922-2020.

Series:

Mathematical surveys and monographs ; no. 61.

Mathematical surveys and monographs, 0076-5376 ; v. 61

Language:

English

Subjects (All):

Boundary value problems.

Differential operators.

Symplectic manifolds.

Physical Description:

xii, 187 pages : illustrations ; 27 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society, [1999]

Contents:

I. Introduction: Fundamental algebraic and geometric concepts applied to the theory of self-adjoint boundary value problems 1

1. Survey of problems, methods, goals: organization of results 1

2. Review of basic definitions and standard results for quasi-differential expressions, and basic concepts of symplectic geometry and symplectic algebra 8

II. Maximal and minimal operators for quasi-differential expressions, and GKN-theory 17

III. Symplectic geometry and boundary value problems 25

1. Symplectic and Lagrangian spaces 25

2. Symplectic geometry applied to boundary value problems 51

IV. Regular boundary value problems 65

V. Singular boundary value problems 79

1. Partition spaces and deficiency indices 79

2. The deficiency index conjecture 85

3. Symplectic invariants of partition and endpoint spaces 90

4. Realizations of deficiency indices: Tabulation of self-adjoint boundary conditions 99

Appendix A. Constructions for quasi-differential operators 109

Appendix B. Complexification of real symplectic spaces, and the real GKN-theory 137.

Notes:

Includes bibliographical references (pages 179-180) and indexes.

ISBN:

0821810804

OCLC:

39189977