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Mat. Zametki, 2002, Volume 72, Issue 1, Pages 54–73 (Mi mz404)  

This article is cited in 1 scientific paper (total in 1 paper)

Nonlinear Commutation Relations: Representations by Point-Supported Operators

M. V. Karasev, E. M. Novikova

Moscow State Institute of Electronics and Mathematics

Abstract: We present a class of non-Lie commutation relations admitting representations by point-supported operators (i.e., by operators whose integral kernels are generalized point-supported functions). For such relations we construct all operator-irreducible representations (up to equivalence). Each representation is realized by point-supported operators in the Hilbert space of antiholomorphic functions. We show that the reproducing kernels of these spaces can be represented via hypergeometric series and the theta function, as well as via their modifications. We construct coherent states that intertwine abstract representations with irreducible representations.

DOI: https://doi.org/10.4213/mzm404

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English version:
Mathematical Notes, 2002, 72:1, 48–65

Bibliographic databases:

UDC: 517.48
Received: 14.01.2002

Citation: M. V. Karasev, E. M. Novikova, “Nonlinear Commutation Relations: Representations by Point-Supported Operators”, Mat. Zametki, 72:1 (2002), 54–73; Math. Notes, 72:1 (2002), 48–65

Citation in format AMSBIB
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\by M.~V.~Karasev, E.~M.~Novikova
\paper Nonlinear Commutation Relations: Representations by Point-Supported Operators
\jour Mat. Zametki
\yr 2002
\vol 72
\issue 1
\pages 54--73
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1942582}
\zmath{https://zbmath.org/?q=an:1048.47053}
\transl
\jour Math. Notes
\yr 2002
\vol 72
\issue 1
\pages 48--65
\crossref{https://doi.org/10.1023/A:1019865004455}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Karasev, E. M. Novikova, “Algebra with Quadratic Commutation Relations for an Axially Perturbed Coulomb–Dirac Field”, Theoret. and Math. Phys., 141:3 (2004), 1698–1724  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математические заметки Mathematical Notes
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