Complex symplectic geometry with applications to ordinary differential operators
Authors:
W. N. Everitt and L. Markus
Journal:
Trans. Amer. Math. Soc. 351 (1999), 49054945
MSC (1991):
Primary 34B05, 34L05; Secondary 47B25, 58F05
Published electronically:
July 20, 1999
MathSciNet review:
1637066
Fulltext PDF Free Access
Abstract 
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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 selfadjoint operators in Hilbert spaces, and this provides an important application of the principal theorems.
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 Everitt, W.N., On the deficiency index problem for ordinary differential operators 19101977, Proceedings of The 1977 Uppsala International Conference: Differential Equations, 6281, Published by the University of Uppsala, Sweden, 1977, distributed by Almquist and Wiksell International Stockholm, Sweden, pp. 6281. MR 57:16788
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 , Linear ordinary quasidifferential expressions, Lecture notes for The Fourth International Symposium on Differential Equations and Differential Geometry, Beijing, Peoples' Republic of China, 128. (Department of Mathematics, University of Peking, Peoples' Republic of China; 1986).
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 Everitt, W.N. and Markus, L., Boundary Value Problems and Symplectic Algebra for Ordinary Differential and QuasiDifferential Operators, Math. Surveys and Monographs, vol. 61, Amer. Math. Soc., Providence, RI, 1999. CMP 99:03
 [EM1]
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 Everitt, W.N. and Race, D., Some remarks on linear ordinary quasidifferential expressions, Proc. London Math. Soc. (3) 54 (1987), 300320. MR 88b:34014
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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:
http://dx.doi.org/10.1090/S0002994799024186
PII:
S 00029947(99)024186
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
