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Mathematics of the USSR-Izvestiya, 1978, Volume 12, Issue 1, Pages 21–51
DOI: https://doi.org/10.1070/IM1978v012n01ABEH001839
(Mi im1690)
 

This article is cited in 10 scientific papers (total in 10 papers)

Carleson series of resonances in the Regge problem

S. A. Ivanov, B. S. Pavlov
References:
Abstract: The scattering problem is investigated for a ystem of differential equations $-y''=k^2Ay$ on the interval $[0,a]$, where $A$ is a positive matrix-valued function which jumps to 1 for $x>a$. The scattering matrix for large spectral parameter is studied, the system of resonances is described, and an expression for the resonance states in terms of the Jost solution is given. A relation is established between the resonances and the poles of the analytic continuation of the Green function. It is proved that the syrtem of resonance states corresponding to complex zeros of the scattering matrix has serial structure; namely, it splits into $n$ Carleson series. The completeness of the system of resonances is investigated, and it is established that this system forms a Riesz basis in the corresponding space with the energy metric.
Bibliography: 23 titles.
Received: 18.05.1976
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1978, Volume 42, Issue 1, Pages 26–55
Bibliographic databases:
UDC: 517.9
MSC: Primary 34B25; Secondary 47A40
Language: English
Original paper language: Russian
Citation: S. A. Ivanov, B. S. Pavlov, “Carleson series of resonances in the Regge problem”, Izv. Akad. Nauk SSSR Ser. Mat., 42:1 (1978), 26–55; Math. USSR-Izv., 12:1 (1978), 21–51
Citation in format AMSBIB
\Bibitem{IvaPav78}
\by S.~A.~Ivanov, B.~S.~Pavlov
\paper Carleson series of resonances in the Regge problem
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 1
\pages 26--55
\mathnet{http://mi.mathnet.ru/im1690}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=486765}
\zmath{https://zbmath.org/?q=an:0375.47021|0401.47020}
\transl
\jour Math. USSR-Izv.
\yr 1978
\vol 12
\issue 1
\pages 21--51
\crossref{https://doi.org/10.1070/IM1978v012n01ABEH001839}
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  • https://doi.org/10.1070/IM1978v012n01ABEH001839
  • https://www.mathnet.ru/eng/im/v42/i1/p26
  • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:441
    Russian version PDF:132
    English version PDF:12
    References:72
    First page:1
     
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