References
S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics [Russian translation], Mir, Moscow (1991).
B. S. Pavlov, “The extension theory and explicitly solvable models,” Uspekhi Mat. Nauk,42, No. 6, 99–131 (1987).
F. A. Berezin and L. D. Faddeev, “A remark on the Schrödinger equation with a singular potential,” Dokl. Akad. Nauk SSSR,137, No. 5, 1011–1014 (1961).
A. G. Kusraev and S. S. Kutateladze, Nonstandard Methods of Analysis [in Russian], Nauka, Novosibirsk (1990).
S. Albeverio, J. E. Fenstad et al., Nonstandard Methods in Stochastic Analysis and Mathematical Physics [Russian translation], Mir, Moscow (1990).
A. I. Baz', Ya. B. Zel'dovich, and A. M. Perelomov, Scattering, Reactions, and Fission in Nonrelativistic Quantum Mechanics [in Russian], Nauka, Moscow (1971).
S. Albeverio, F. Gesztesy, R. Høegh-Krohn, and L. Streit, “Charged particles with short-range interactions,” Ann. Inst. H. Poincaré Anal. Non Linéaire,38, No. 3, 263–293 (1983).
V. A. Geiler, “The two-dimensional Schrödinger operator with a homogeneous magnetic field and the perturbations of the operator by periodic potentials of radius zero,” Algebra i Analiz,3, No. 3, 1–48 (1991).
Y. B. Levinson, M. I. Lubin, and E. V. Sukhorukov, “Short-range impurity in a saddle-point potential,” Phys. Rev. B(3),45, No. 20, 11936–11943 (1992).
J. C. Maan, “Combined electric and magnetic field effects in semiconductors heterostructures,” Springer Ser. Solid-State Sci.,53, 183–191 (1984).
Yu. E. Karpeshina, “The spectrum and eigenfunctions of the Schrödinger operator with a point potential of homogeneous lattice type in three-dimensional space,” Teoret. Mat. Fiz.,57, No. 2, 304–313 (1983).
M. G. Krein and G. K. Langer, “On defect subspaces and generalized resolvents of a Hermitian operator in the space Πℵ,” Funktsional. Anal. i Prilozhen.,5, No. 2, 59–71 (1971).
V. A. Geiler and V. A. Margulis, “The Anderson localization in the nondiscrete Maryland model,” Teoret. Mat. Fiz.,70, No. 2, 192–201 (1987).
A. V. Bukhvalov, “Applications of the methods of the theory of order bounded operators in theL p spaces,” Uspekhi Mat. Nauk,38, No. 6, 37–83 (1983).
V. B. Korotkov, Integral Operators [in Russian], Nauka, Novosibirsk (1983).
Yu. G. Shondin, “Quantum-mechanical models in ℝn related to the extensions of the energy operator in Pontryagin space,” Teoret. Mat. Fiz.,74, No. 3, 331–344 (1988).
I. Yu. Popov, “Justification of a model of zero width slots for the Dirichlet problem,” Sibirsk. Mat. Zh.,30, No. 3, 103–108 (1989).
A. N. Kochubei, “Elliptic operators with boundary conditions on a subset of measure zero,” Funktsional. Anal. i Prilozhen.,16, No. 2, 74–75 (1982).
J. Zorbas, “Perturbation of self-adjoint operators by Dirac distributions,” J. Math. Phys.,21, No. 4, 840–847 (1980).
M. M. Day, Normed Linear Spaces [Russian translation], Izdat. Inostr. Lit., Moscow (1961).
I. Ts. Gokhberg and S. G. Krein, Introduction to the Theory of Nonselfajoint Linear Operators in Hilbert Space [in Russian], Nauka, Moscow (1965).
P. R. Halmos and V. S. Sunder, Bounded Integral Operators onL 2 Spaces [Russian translation], Nauka, Moscow (1985).
B. Simon, “Schrödinger semigroups,” Bull. Amer. Math. Soc.,7, No. 3, 447–526 (1982).
H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger Operators with Applications to Quantum Mechanics and Global Geometry [Russian translation], Mir, Moscow (1990).
E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations Vol. I and II [Russian translation], Izdat. Inostr. Lit., Moscow (1960, 1961).
H. Bateman and A. Erdélyi, Higher Transcendental Functions. Vol. I and II [Russian translation], Nauka, Moscow (1973, 1974).
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Translated fromSibirskii Matematicheskii Zhurnal, Vol. 36, No. 4, pp. 828–841, July–August, 1995.
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Geiler, V.A., Margulis, V.A. & Chuchaev, I.I. Potentials of zero radius and Carleman operators. Sib Math J 36, 714–726 (1995). https://doi.org/10.1007/BF02107328
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DOI: https://doi.org/10.1007/BF02107328