Sturm-liouville operators with singular potentials

B. M. Levitan and I. S. Sargsyan,Introduction to Spectral Theory of Operators [in Russian], Nauka, Moscow (1970).

M. A. Naimark,Linear Differential Operators [in Russian], Nauka, Moscow (1969).

L. D. Landau and E. M. Lifshits,Theoretical Physics, Vol. 3.Quantum Mechanics, Nonrelativistic Theory [in Russian], Nauka, Moscow (1989).

F. A. Berezin and L. D. Faddeev, “Remarks on the Schrödinger equation with singular potential,”Dokl. Akad. Nauk SSSR, [Soviet Math. Dokl.],137, No. 7, 1011–1014 (1961).

R. A. Minlos and L. D. Faddeev, “On point interaction for three particle systems in quantum mechanics,”Dokl. Akad. Nauk SSSR, [Soviet Math. Dokl.],141, No. 6, 1335–1338 (1961).

F. A. Berezin, “On the Lie model,”Mat. Sb. [Math. USSR-Sb.], No. 4, 425–446 (1963).

F. Gesztezy and B. Simon, “Rank-one perturbations at infinite coupling,”J. Funct. Anal.,128, 245–252 (1995).

A. Kiselev and B. Simon, “Rank one perturbations with infinitesimal coupling,”J. Funct. Anal.,130, 345–356 (1995).

V. Koshmanenko, W. Karwowski and S. Ota, “Schrödinger operator perturbed by operators related to null-sets,”Positivity,2, No. 1, 77–99 (1998).

S. Albaverio, F. Gestezy, R. Hoegh-Krohn, and H. Holden,Some Exactly Solvable Models in Quantum Mechanics, Springer, Berlin-New York (1988).

V. D. Koshmanenko, “Perturbations of self-adjoint operators by singular sesquilinear forms,”Ukrain. Mat. Zh. [Ukrainian Math. J.],41, No. 1, 3–19 (1989).

A. K. Fragela, “On perturbations of the polyharmonic operator by potentials supported by sets of zero measure,”Dokl. Akad. Nauk SSSR [Soviet Math. Dokl.],245, No. 1, 34–36 (1979).

Yu. G. Shondin, “Perturbations on thin sets of high codimension of elliptic operators and extension theory in the space with indefinite metric,”Zap. Nauchn. Sem. St. Petersburg. Otdel. Mat. Inst. Steklov (POMI) [in Russian], Vol. 222,Investigations on Linear Operators and Theory of Functions, No. 23 (1995), pp. 246–292, 310–311.

J. Gunson, “Perturbation theory for a Sturm-Liouville problem with an interior singularity,”Proc. Roy. Soc. London Ser. A,414, 255–269 (1987).

P. Kurasov, “On the Coulomb potentials in one dimensions,”J. Phys. A,29, No. 8, 1767–1771 (1996).

M. Reed and B. Simon,Methods of Modern Mathematical Physics, Vol. 2, Academic Press, New York-San Francisko-London (1975).

M. I. Neiman-zade and A. A. Shkalikov, “Shrödinger operators with singular potentials from the spaces of multipliers,”Mat. Zametki [Math. Notes],66, No. 5, 723–733 (1999).

T. Kato,Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-Heidelberg-New York (1966).

M. G. Krein, “Theory of self-adjoint extensions of semibounded operators and its applications, I II,”Mat. Sb. [Math. USSR-Sb.],21, No. 3, 365–404 (1947).

P. Halmos,A Hilbert Space Problem Book, Toronto-London (1967).

I. Gokhberg and M. G. Krein,Introduction on the Theory of Linear Nonself-adjoint Operators in Hilbert Space [in Russian], Nauka, Moscow (1965).

M. V. Keldysh, “On the completeness of eignefunctions for some classes of nonself-adjoint linear operators,”Uspekhi Mat. Nauk [Russian Math. Surveys],26, No. 4, 295–305 (1971).

E. L. Ince,Ordinary Differential Equations, 2nd ed. Dover Publ., New York, (1956).

Ph. Hartman,Ordinary Differential Equations, New York-London-Sydney (1964).

P. Seba, “Some remarks on the δ-interaction in one dimension,”Rep. Math. Phys.,24, No. 1, 111–120 (1986).

I. M. Gel’fand, and G. E. Shilov,The Generalized Functions and Operations With Them [in Russian], Fizmatgiz, Moscow (1959).