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TMF, 1998, Volume 116, Number 2, Pages 163–181 (Mi tmf895)  

This article is cited in 5 scientific papers (total in 5 papers)

Operator interpretation of the resonances generated by ${2}\times {2}$ matrix Hamiltonians

R. Mennickena, A. K. Motovilovb

a Universität Regensburg
b Joint Institute for Nuclear Research, Bogoliubov Laboratory of Theoretical Physics

Abstract: An analytic continuation of the transfer function for a $2\times 2$ matrix Hamiltonian to unphysical sheets of the Riemann energy surface is considered. Nonselfadjoint operators are constructed such that their spectra reproduce certain parts of the transfer-function spectrum including resonances on the unphysical sheets nearest to the physical one. The basis property and completeness of the systems of transfer-function root vectors, which include resonance vectors, are established.

DOI: https://doi.org/10.4213/tmf895

Full text: PDF file (322 kB)

English version:
Theoretical and Mathematical Physics, 1998, 116:2, 867–880

Bibliographic databases:

Received: 01.01.1998

Citation: R. Mennicken, A. K. Motovilov, “Operator interpretation of the resonances generated by ${2}\times {2}$ matrix Hamiltonians”, TMF, 116:2 (1998), 163–181; Theoret. and Math. Phys., 116:2 (1998), 867–880

Citation in format AMSBIB
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\paper Operator interpretation of the resonances generated by ${2}\times {2}$ matrix Hamiltonians
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\jour Theoret. and Math. Phys.
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Derezinski, J, “Spectral theory of Pauli-Fierz operators”, Journal of Functional Analysis, 180:2 (2001), 243  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. Hardt, V, “A factorization theorem for the transfer function associated with a 2 x 2 operator matrix having unbounded couplings”, Journal of Operator Theory, 48:1 (2002), 187  mathscinet  zmath  isi
    3. A. A. Arsen'ev, “Mathematical Model of Resonances and Tunneling in a System with a Bound State”, Theoret. and Math. Phys., 136:3 (2003), 1336–1345  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. Albeverio, S, “Graph subspaces and the spectral shift function”, Canadian Journal of Mathematics-Journal Canadien de Mathematiques, 55:3 (2003), 449  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Huber, M, “SPECTRAL ANALYSIS OF RELATIVISTIC ATOMS - INTERACTION WITH THE QUANTIZED RADIATION FIELD”, Documenta Mathematica, 14 (2009), 115  mathscinet  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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