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ABSTRACT
In this paper, we give a correct definition of the Laplace operator with delta-like potentials. Correctly solvable pointwise perturbation is investigated and formulas of resolvent are described. We study some properties of the resolvent. In particular, we prove Krein's formula for these resolvents.
Acknowledgments
Authors thank the anonymous referees for reading the paper carefully and providing thoughtful comments, which improved the exposition of the paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The work was partially supported by the grants of the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan [grant number AP08855402 and AP09258335].