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Zap. Nauchn. Sem. POMI, 2005, Volume 327, Pages 25–54 (Mi znsl322)  

Invariant transformations for the Sturm–Liouville operator

A. Vagharshakyan

Institute of Mathematics, National Academy of Sciences of Armenia

Abstract: In this paper we consider the Sturm–Liouville operator on a finite interval. For particular boundary conditions, a group of invariant transformations that preserve the operator's spectrum is constructed. This result permits us to reconsider some old problems for the Sturm–Liouville operator. In particular, the influence of this group on the inverse problem is discussed.

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English version:
Journal of Mathematical Sciences (New York), 2006, 139:2, 6374–6392

Bibliographic databases:

UDC: 517.948
Received: 27.03.2005
Language:

Citation: A. Vagharshakyan, “Invariant transformations for the Sturm–Liouville operator”, Investigations on linear operators and function theory. Part 33, Zap. Nauchn. Sem. POMI, 327, POMI, St. Petersburg, 2005, 25–54; J. Math. Sci. (N. Y.), 139:2 (2006), 6374–6392

Citation in format AMSBIB
\Bibitem{Vag05}
\by A.~Vagharshakyan
\paper Invariant transformations for the Sturm--Liouville operator
\inbook Investigations on linear operators and function theory. Part~33
\serial Zap. Nauchn. Sem. POMI
\yr 2005
\vol 327
\pages 25--54
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl322}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2184427}
\zmath{https://zbmath.org/?q=an:1136.34066}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2006
\vol 139
\issue 2
\pages 6374--6392
\crossref{https://doi.org/10.1007/s10958-006-0355-8}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33750163361}


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