Abstract:
Dissipative Schrödinger operators are studied in Weyl's limit-circle case. A selfadjoint dilation and a spectral model of these operators are constructed and the characteristic function is computed. Theorems on the completeness of the eigenfunctions of the dissipative operators are proved.
Citation:
B. P. Allakhverdiev, “On dilatation theory and spectral analysis of dissipative Schrodinger operators in Weyl's limit-circle case”, Math. USSR-Izv., 36:2 (1991), 247–262
\Bibitem{All90}
\by B.~P.~Allakhverdiev
\paper On~dilatation theory and spectral analysis of dissipative Schrodinger operators in Weyl's limit-circle case
\jour Math. USSR-Izv.
\yr 1991
\vol 36
\issue 2
\pages 247--262
\mathnet{http://mi.mathnet.ru/eng/im1092}
\crossref{https://doi.org/10.1070/IM1991v036n02ABEH002020}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1062512}
\zmath{https://zbmath.org/?q=an:0728.47003}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?1991IzMat..36..247A}
Linking options:
https://www.mathnet.ru/eng/im1092
https://doi.org/10.1070/IM1991v036n02ABEH002020
https://www.mathnet.ru/eng/im/v54/i2/p242
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Aytekin Ery{\i}lmaz, Hüseyin Tuna, “Spectral analysis of dissipative fractional Sturm–Liouville operators”, Georgian Mathematical Journal, 24:3 (2017), 351
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Ekin Uğurlu, Elgiz Bairamov, “Dissipative operators with impulsive conditions”, J Math Chem, 2013
Ekin Uğurlu, Elgiz Bairamov, “Spectral analysis of eigenparameter dependent boundary value transmission problems”, Journal of Mathematical Analysis and Applications, 2013
Bilender P. Allahverdiev, Elgiz Bairamov, Ekin Ugurlu, “Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions”, Journal of Mathematical Analysis and Applications, 2012
J. Behrndt, M. Langer, Operator Methods for Boundary Value Problems, 2012, 121
M. Yakít Ongun, Bilender P. Allahverdiev, “A completeness theorem for a dissipative Schrödinger problem with the spectral parameter in the boundary condition”, Math Nachr, 281:4 (2008), 541
M. Yak{\i}t Ongun, “Spectral analysis of nonselfadjoint Schrödinger problem with eigenparameter in the boundary condition”, Sci China Ser A, 50:2 (2007), 217
Ryzhov V., “Functional Model of a Class of Non-Selfadjoint Extensions of Symmetric Operators”, Operator Theory, Analysis and Mathematical Physics, Operator Theory : Advances and Applications, 174, eds. Janas J., Kurasov P., Laptev A., Naboko S., Stolz G., Birkhauser Verlag Ag, 2007, 117–158
B. P. Allakhverdiev, “On the theory of nonselfadjoint operators of Schrödinger type with a matrix potential”, Russian Acad. Sci. Izv. Math., 41:2 (1993), 193–205
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