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Contemporary Mathematics. Fundamental Directions, 2006, Volume 16, Pages 22–37 (Mi cmfd46)  
On topological properties of manifolds of eigenfunctions generated by a family of periodic Sturm–Liouville problems

Ya. M. Dymarskii

Luhansk Taras Schevchenko State Pedagogical University
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Abstract: In the paper, we study manifolds of eigenfunctions of a fixed oscillation. Then, solving the trivial inverse problem of reconstruction of a potential by an eigenfunction, we describe the properties of manifolds of potentials. The approach proposed allows one to link topological properties of manifolds of eigenfunctions with those of manifolds of potentials.
English version:
Journal of Mathematical Sciences, 2008, Volume 149, Issue 5, Pages 1488–1503
DOI: https://doi.org/10.1007/s10958-008-0078-0
Bibliographic databases:
UDC: 517.927.25+517.984.55
Language: Russian
Citation: Ya. M. Dymarskii, “On topological properties of manifolds of eigenfunctions generated by a family of periodic Sturm–Liouville problems”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 2, CMFD, 16, PFUR, M., 2006, 22–37; Journal of Mathematical Sciences, 149:5 (2008), 1488–1503
Citation in format AMSBIB
\Bibitem{Dym06}
\by Ya.~M.~Dymarskii
\paper On topological properties of manifolds of eigenfunctions generated by a~family of periodic Sturm--Liouville problems
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~2
\serial CMFD
\yr 2006
\vol 16
\pages 22--37
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd46}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336443}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 5
\pages 1488--1503
\crossref{https://doi.org/10.1007/s10958-008-0078-0}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84920848235}
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