Complex symplectic geometry with applications

to ordinary differential operators

Authors:
W. N. Everitt and L. Markus

Journal:
Trans. Amer. Math. Soc. **351** (1999), 4905-4945

MSC (1991):
Primary 34B05, 34L05; Secondary 47B25, 58F05

DOI:
https://doi.org/10.1090/S0002-9947-99-02418-6

Published electronically:
July 20, 1999

MathSciNet review:
1637066

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Complex symplectic spaces, and their Lagrangian subspaces, are defined in accord with motivations from Lagrangian classical dynamics and from linear ordinary differential operators; and then their basic algebraic properties are established. After these purely algebraic developments, an Appendix presents a related new result on the theory of self-adjoint operators in Hilbert spaces, and this provides an important application of the principal theorems.

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Additional Information

**W. N. Everitt**

Affiliation:
Department of Mathematics and Statistics, University of Birmingham, Birmingham B15 2TT, England, United Kingdom

Email:
w.n.everitt@bham.ac.uk

**L. Markus**

Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

Email:
markus@math.umn.edu

DOI:
https://doi.org/10.1090/S0002-9947-99-02418-6

Keywords:
Ordinary linear differential operators,
deficiency indices,
symmetric boundary conditions,
symplectic geometry

Received by editor(s):
August 19, 1997

Published electronically:
July 20, 1999

Dedicated:
Dedicated to Professor Hugh L. Turrittin on the occasion of his ninetieth birthday

Article copyright:
© Copyright 1999
American Mathematical Society