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Mat. Zametki, 1997, Volume 62, Issue 2, Pages 206–215 (Mi mz1605)  

This article is cited in 7 scientific papers (total in 7 papers)

On a transformation operator

I. M. Guseinov

Baku State University

Abstract: We prove the existence of a transformation operator that takes the solution of the equation $y-\lambda^{2n}y$ to the solution of the equation
$$ y"-(q_0(x)+\lambda q_1(x)+…+\lambda^{n-1}q_{n-1}(x))y=\lambda^{2n}y $$
with a condition at infinity. Some properties of the kernel of this operator are studied.

DOI: https://doi.org/10.4213/mzm1605

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English version:
Mathematical Notes, 1997, 62:2, 172–180

Bibliographic databases:

UDC: 517.9
Received: 15.08.1995

Citation: I. M. Guseinov, “On a transformation operator”, Mat. Zametki, 62:2 (1997), 206–215; Math. Notes, 62:2 (1997), 172–180

Citation in format AMSBIB
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\by I.~M.~Guseinov
\paper On a transformation operator
\jour Mat. Zametki
\yr 1997
\vol 62
\issue 2
\pages 206--215
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\crossref{https://doi.org/10.4213/mzm1605}
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\zmath{https://zbmath.org/?q=an:0921.34075}
\transl
\jour Math. Notes
\yr 1997
\vol 62
\issue 2
\pages 172--180
\crossref{https://doi.org/10.1007/BF02355905}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000071268600024}


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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. Guseinov, IM, “Transformation operators and asymptotic formulas for the eigenvalues of a polynomial pencil of Sturm-Liouville operators”, Siberian Mathematical Journal, 41:3 (2000), 453  mathnet  crossref  mathscinet  isi  scopus  scopus
    2. Bascanbaz-Tunca, G, “Spectral properties of a Schrodinger equation with a class of complex potentials and a general boundary condition”, Journal of Mathematical Analysis and Applications, 286:1 (2003), 207  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Agamaliyev, A, “On eigenvalues of some boundary value problems for a polynomial pencil of Sturm-Liouville equation”, Applied Mathematics and Computation, 165:3 (2005), 503  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Nabiev, AA, “Inverse scattering problem for the Schrodinger-type equation with a polynomial energy-dependent potential”, Inverse Problems, 22:6 (2006), 2055  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    5. Nabiev, AA, “On the Jost solutions of the Schrodinger-type equations with a polynomial energy-dependent potential”, Inverse Problems, 22:1 (2006), 55  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    6. Nabiev A.A., “On a Fundamental System of Solutions of the Matrix Schrodinger Equation with a Polynomial Energy-Dependent Potential”, Math. Meth. Appl. Sci., 33:11 (2010), 1372–1383  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. V. V. Katrakhov, S. M. Sitnik, “Metod operatorov preobrazovaniya i kraevye zadachi dlya singulyarnykh ellipticheskikh uravnenii”, Singulyarnye differentsialnye uravneniya, SMFN, 64, no. 2, Rossiiskii universitet druzhby narodov, M., 2018, 211–426  mathnet  crossref
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