Abstract
Singular relatively compact perturbations of self-adjoint operators are studied. The results obtained are applied to the Schrödinger operator with a singular potential.
Similar content being viewed by others
References
S. Albeverio et al., Solvable Models in Quantum Mechanics, Springer-Verlag, New York (1988).
Yu. M. Berezansky, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables [in Russian], Naukova Dumka, Kyiv (1978).
I. Ts. Gokhberg and M. G. Krein, Introduction to the Theory of Linear Non-Self-Adjoint Operators [in Russian], Nauka, Moscow (1965).
I. Ts. Gokhberg and E. I. Sigal, “Operator generalization of the theorem on logarithmic residues and the Rouche theorem, ” Mat. Sb., 84, No. 4 (1971); English transl. in Math. USSR-Sb.
T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin-New York (1966).
J.-L. Lions and E. Madźenes, Nonhomogeneous Boundary Value Problems and Their Applications, Russian translation from the French (V. V. Grušin, ed.), Mir, Moscow (1971).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Mathematical Analysis [in Russian], Nauka, Moscow (1989).
Ya. Mykytyuk and Yu. Djala, “Singular perturbations of closed operators, ” Math. Studies, Transactions of the Lviv Mathematical Society, 11, No. 1.
J. Brasche, “On the spectral properties of singular perturbed operators, ” in: Dirichlet Forms and Stochastic Processes, (Beijing, 1993), de Gruyter, Berlin (1995), pp. 65–72.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mykytyuk, Y.V., Djala, U.S. Singular Perturbations of Self-Adjoint Operators. Journal of Mathematical Sciences 107, 3583–3591 (2001). https://doi.org/10.1023/A:1011942207113
Issue Date:
DOI: https://doi.org/10.1023/A:1011942207113