Abstract
In present paper we proved that the operator generated by the differential expression of second order with fractional derivative in lower terms, does not generate associated functions and that the system of eigenfunctions of this operator forms a basis in L 2(0, 1).
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References
M. V. Keldysh, On the eigenvalues and eigenfunctions of some classes of equations nesamosopryazhnnyh (Dokl. USSR Academy of Sciences, 1951), p. 11–14 [In Russian].
M. V. Keldysh, Uspekhi Mat. Sciences. 26 (4), 15–41 (1971).
D. Ingman and J. Suzdalnitsky, Comp.Methods Appl.Mech. Engrg. 190, 5027–5036 (2001).
A. M. Nahushev, Fractional calculus and its application (FIZMATLIT, 2003) [In Russian].
E. A. Larionov, E. M. Zveryaev, and T. S. Aleroev, On the theory of weak perturbations of normal operators (Preprint 14, Moscow, 2014).
T. S. Aleroev, Boundary problems for differential equations with fractional derivatives (Diss. Doctor of Physics and Mathematics. Sciences, Moscow State University, 2000).
T. S. Aleroev and M. Tan Y.-F. Kirane, Ukrainian Mathematical Bulletin 10 (2), 158–175 (2013).
B. V. Loginov, 6, 14–19, (1963).
T. Kato, Perturbation theory for linear operators (Mir, Moscow, 1972).
T. S. Aleroev, 11(25), 1996–1997 (1989).
T. S. Aleroev, Boundary problems for differential equations with fractional derivatives (PhD thesis in Phys. and Math. Sciences, Baku, 1983).
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Submitted by O. E. Tikhonov
An erratum to this article is available at http://dx.doi.org/10.1134/S1995080216060214.
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Aleroev, T.S., Aleroeva, H.T. On the eigenfunctions and eigenvalues of a class of non-selfadjoint operators. Lobachevskii J Math 37, 227–230 (2016). https://doi.org/10.1134/S1995080216030082
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DOI: https://doi.org/10.1134/S1995080216030082