Far Eastern Mathematical Journal

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About generalized resolvent of one integro-diferential operator of the second order on semiaxis


G. I. Sin'ko

2005, issue 1-2, Ń. 71–81


Abstract
In this article a symmetrical integro-differential operator of the second order on semiaxis is considered. Its quasiselfadjoint extension is described, and the formula for all generalized resolvents of this operator in $L_2(0,+\infty)$ is constructed. It also prooves that any generalized resolvent $R_\lambda$ is an integral operator for any nonreal $\lambda$.

Keywords:
integro-differential operator, generalized resolvents

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References

[1] N. I. Axiezer, I. N. Glazman, Teoriya linejnyx operatorov v gil'bertovom prostranstve, Nauka, M., 1966, 543 s.
[2] O. P. Kruglikova, “Obobshhennye rezol'venty i spektral'nye funkcii odnogo integro-differencial'nogo operatora pervogo poryadka v prostranstve vektornoznachnyx funkcij”, Funkcional'nyj analiz, mezhvuz. sb., Ul'yanovsk, 1997, 24–30.
[3] G. I. Sin'ko, “Ob obobshhennoj rezol'vente odnogo integro-differencial'nogo operatora”, Dal'nevostochnyj matematicheskij sbornik, 6, Dal'nauka, Vladivostok, 1998, 57–63.
[4] G. I. Sin'ko, Spektral'naya teoriya integro-differencial'nyx operatorov v gil'bertovom prostranstve, Izd-vo UGPI, Ussurijsk, 1999, 151 s.
[5] A. V. Cyganov, “O spektral'nyx razlozheniyax operatorov differencirovaniya”, Funkcional'nyj analiz, mezhvuz. sb., U l'yanovsk, 1999, 53–63.
[6] A. V. Shtraus, “O spektral'nyx funkciyax differencial'nyx operatorov”, Izv. AN SSSR. Ser. mat., 19:4 (1955), 201–220.
[7] A. V. Shtraus, “Obobshhennye rezol'venty simmetricheskix operatorov”, Izv. AN SSSR. Ser. Mat., 18:1 (1954), 51–86.

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