Complex symplectic geometry with applications to ordinary differential operators

Everitt, W.; Markus, L.

doi:10.1090/S0002-9947-99-02418-6

Complex symplectic geometry with applications to ordinary differential operators
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by W. N. Everitt and L. Markus

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

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

Published electronically: July 20, 1999

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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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