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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
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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