Correctness of the definition of the Laplace operator with delta-like potentials

References

• Pavlov BS. The theory of extensions and explicitly-soluble models. Russian Math Surveys. 1987;42(6):127–168.
   Web of Science ®Google Scholar
• Albeverio S, Kurasov P. Singular perturbations of differential operators. Solvable Schrdinger type operators. Cambridge: Cambridge University Press; 2000. xiv+429 pp. (London Mathematical Society Lecture Note Series; 271).
   Google Scholar
• Blanchard Ph., Figari R, Mantile A. Point interaction Hamiltonians in bounded domains. J Math Phys. 2007;48:082108. doi:10.1063/1.2770672.
   Google Scholar
• Sh. Birman M, Suslina TA, Shterenberg RG. Absolute continuity of the two-dimensional Schrödinger operator with delta potential concentrated on a periodic system of curves. St Petersburg Math J. 2001;12(6):983–1012.
   Google Scholar
• Fragela AK. On perturbation of a polyharmonic operator by delta-like potentials. Math USSR-Sb. 1987;58(2):389–396.
   Google Scholar
• Kurasov P. Triplet extensions I: semibounded operators in the scale of Hilbert spaces. J Anal Math. 2009;107:251–286.
   Web of Science ®Google Scholar
• Savchuk AM, Shkalikov AA. Sturm–Liouville operators with singular potentials. Math Notes. 1999;66(6):741–753.
   Web of Science ®Google Scholar
• Albeverio S, Gesztesy F, Høegh-Krohn R, et al. Solvable models in quantum mechanics. In: Exner P, editor, With an appendix. 2nd ed. Providence, RI: AMS Chelsea Publishing; 2005. xiv+488 pp.
   Google Scholar
• Berezin FA, Faddeev LD. Remark on the Schrödinger equation with singular potential. Soviet Phys Dokl. 1961;2:372–375.
   Google Scholar
• Kanguzhin BE, Aniyarov AA. Well-posed problems for the Laplace operator in a punctured disk. Math Notes. 2011;89(6):819–829.
   Web of Science ®Google Scholar
• Kanguzhin BE, Nurakhmetov DB, Tokmagambetov NE. Laplace operator with δ-like potentials. Russian Math. 2014;58(2):6–12.
   Google Scholar
• Kanguzhin BE, Tokmagambetov NE. Resolvents of well-posed problems for finite-rank perturbations of the polyharmonic operator in a punctured domain. Siberian Math J. 2016;57(2):265–273.
   Web of Science ®Google Scholar
• Kanguzhin BE, Tokmagambetov NE. On regularized trace formulas for a well-posed perturbation of the m-Laplace operator. Differ Equ. 2015;51(12):1583–1588.
   Web of Science ®Google Scholar
• Kanguzhin BE, Tulenov KS. Singular perturbations of Laplace operator and their resolvents. Complex Var. Elliptic Equ. 2020;65(9):1433–1444.
   Web of Science ®Google Scholar
• Kanguzhin BE, Tokmagambetov NE. A regularized trace formula for a well-perturbed Laplace operator. Doklady Math. 2015;91(1):1–4.
   Web of Science ®Google Scholar
• Courant R, Hilbert D. Methods of mathematical physics. Partial differential equations. Vol. II. New York (NY): Interscience; 1962. p. xxii+830.
   Google Scholar
• Olenik OA. Lectures on partial differential equations. 2nd ed., Moscow: Moskov. Gos. Univ., Mekh.-Mat. Fak.; 2005. p. 260 (Russian).
   Google Scholar
• Sh. Birman M, Suslina TA. Second order periodic differential operators. threshold properties and homogenization. St Petersburg Math J. 2004;15(5):639–714.
   Google Scholar
• Sh. Birman M, Yafaev DR. The spectral shift function. the papers of M. G. Kren and their further development. St Petersburg Math J. 1993;4(5):833–870.
   Google Scholar
• Gohberg IC, Kren MG. Introduction to the theory of linear non-selfadjoint operators. Providence (RI): American Mathematical Society; 1969. (Translations of Mathematical Monographs; 18).
   Google Scholar
• ljljljlKanguzhin BE, Dauitbek D. A maximum of the first eigenvalue of semibounded differential operator with a parameter. Russian Math. 2017;61(2):10–16.
   Web of Science ®Google Scholar
• Crum MM. Associated Sturm-Liouville systems. Quart S Math. 1955;6:121–127.
   Google Scholar
• Gilbert RC, Kramer VA. Trace formulas for a perturbed operator. Duke Math J. 1963;30(2):275–296.
   Web of Science ®Google Scholar
• Gilbert RC, Kramer VA. Trace formulas for powers of a Styrm–Liouville operator. Canad J Math. 1964;16(4):412–422.
   Google Scholar