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Mathematics of the USSR-Izvestiya, 1991, Volume 36, Issue 2, Pages 281–309
DOI: https://doi.org/10.1070/IM1991v036n02ABEH002022
(Mi im1094)
 

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
References:
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
Bibliographic databases:
Document Type: Article
UDC: 513.015.7, 512.625.5
MSC: Primary 35P05, 81C40, 81C99; Secondary 46P05
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
\Bibitem{VlaVolZel90}
\by V.~S.~Vladimirov, I.~V.~Volovich, E.~I.~Zelenov
\paper Spectral theory in $p$-adic quantum mechanics, and representation theory
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 2
\pages 281--309
\mathnet{http://mi.mathnet.ru//eng/im1094}
\crossref{https://doi.org/10.1070/IM1991v036n02ABEH002022}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1062514}
\zmath{https://zbmath.org/?q=an:0715.22029|0709.22010}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..281V}
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  • https://doi.org/10.1070/IM1991v036n02ABEH002022
  • https://www.mathnet.ru/eng/im/v54/i2/p275
  • This publication is cited in the following 29 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
     
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