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This article is cited in 27 scientific papers (total in 29 papers)
Spectral theory in $p$-adic quantum mechanics, and representation theory
V. S. Vladimirov, I. V. Volovich, E. I. Zelenov
Abstract:
Spectral theory is discussed for a harmonic oscillator in $p$-adic quantum mechanics. The problem of the decomposition into irreducible representations of the restriction of a projective representation of the symplectic group to a compact abelian subgroup is solved, the dimensions of the invariant subspaces are calculated, and the eigenfunctions are analyzed. Spectral problems are considered for $p$-adic pseudodifferential operators of Schrödinger type. A complete orthonormal system of eigenfunctions is constructed for the $p$-adic analog of the differentiation operator.
Received: 12.10.1989
Citation:
V. S. Vladimirov, I. V. Volovich, E. I. Zelenov, “Spectral theory in $p$-adic quantum mechanics, and representation theory”, Math. USSR-Izv., 36:2 (1991), 281–309
Linking options:
https://www.mathnet.ru/eng/im1094https://doi.org/10.1070/IM1991v036n02ABEH002022 https://www.mathnet.ru/eng/im/v54/i2/p275
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