Symplectic classification of quadratic forms, and general Mehler formulas
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Publication:1897996
DOI10.1007/BF02572374zbMath0829.35150WikidataQ110898058 ScholiaQ110898058MaRDI QIDQ1897996
Publication date: 15 January 1996
Published in: Mathematische Zeitschrift (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/174782
normal formsWeyl operatorMehler formulaAvron-Herbst formulaWeyl symbolStark operatorHamilton mapcomplete classification of quadratic forms in a symplectic vector spaceinhomogeneous quadratic forms
Pseudodifferential operators as generalizations of partial differential operators (35S05) Quadratic forms over global rings and fields (11E12) Fourier integral operators applied to PDEs (35S30)
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Cites Work
- Unnamed Item
- Unnamed Item
- \(L^ 2\) estimates for Fourier integral operators with complex phase
- Spectral and scattering theory of Schrödinger operators related to the Stark effect
- The behavior of the index of a periodic linear Hamiltonian system under iteration
- Canonical forms for symplectic and Hamiltonian matrices
- On the Algebraic Problem Concerning the Normal Forms of Linear Dynamical Systems