Literature Cited
M. Reed and B. Simon, Methods of Modern Mathematical Physics. II. Fourier Analysis, Self-Adjointness, Academic Press, New York (1975).
W. M. Frank, D. J. Land, and R. M. Spector “Singular potentials” Rev. Mod. Phys.,43, No. 1, 36–98 (1971).
M. A. Naimark, Linear Differential Operators [in Russian], Nauka, Moscow (1969).
C. T. Fulton, “Parametrization of Titchmarsh's m(λ)-functions in the limit-circle case,” Trans. Am. Math. Soc.,229, 51–63 (1977).
F. Rellich, “Halbbeschränkte gewöhnliche Differential-operatoren zweiter Ordnung,” Math. Ann.,122, 343–368 (1951).
F. Rellich, “Die zulässigen Randbedingungen bei den singulären Eigenwertproblemen der mathematischen Physik,” Math. Z.,49, 702–723 (1943/44).
C. Burnap, W. Greenberg, P. F. Zweifel, “Eigenvalue problem for singular potentials,” Nuovo Cimento A,50, No. 4, 457–465 (1979).
W. Bulla and F. Gesztesy, “Deficiency indices and singular boundary conditions in quantum mechanics,” J. Math. Phys.,26, No. 10, 2520–2528 (1985).
F. W. J. Olver, Asymptotics and Special Functions, Academic Press, New York (1974).
H. Behncke and H. Focke, “Deficiency indices of singular Schrödinger operators,” Math. Z.,158, 87–98 (1978).
A. N. Kochubei, “Symmetric operators and nonclassical spectral problems,” Mat. Zametki,25, No. 3, 425–434 (1979).
V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
B. S. Pavlov, “Theory of extensions and explicitly-solvable models,” Usp. Mat. Nauk,42, No. 6, 99–131 (1987).
Ph. Hartman, Ordinary Differential Equations, 2nd edn., Birkhäuser, Boston (1982).
M. Bairamogly, “On self-adjoint extensions of an operator equation with a singularity,” Izv. Akad. Nauk Az. SSR, Ser. Fiz.-Tekh. Mat. Nauk, No. 2, 140–143 (1976).
V. A. Derkach and M. M. Malamud, “On Weyl functions and Hermitian operators with lacunas,” Dokl. Akad. Nauk SSSR,293, No. 5, 1041–1046 (1987).
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Kiev. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 60–69, May–June, 1991.
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Kochubei, A.N. Self-adjoint extensions of a Schrödinger opertor with singular potential. Sib Math J 32, 401–409 (1991). https://doi.org/10.1007/BF00970475
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DOI: https://doi.org/10.1007/BF00970475