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Zeitschrift für Analysis und ihre Anwendungen


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Volume 31, Issue 2, 2012, pp. 125–137
DOI: 10.4171/ZAA/1451

Published online: 2012-03-30

Regular Potential Approximation for $\delta$-Perturbation Supported by Curve of the Laplace-Beltrami Operator on the Sphere

D.A. Eremin[1], D.A. Ivanov[2] and Igor Yu. Popov[3]

(1) Mordovian State University, Saransk, Russian Federation
(2) Mordovian State University, Saransk, Russian Federation
(3) St. Petersburg National Research University of Information Technologies, Mechanics and Optics, Russian Federation

Operator extension theory model for -perturbation supported by curve of the Laplace-Beltrami operator on the sphere is described. The sequence of operators with regular potentials converging to the model operator in norm resolvent sense is constructed.

Keywords: Laplace-Beltrami operator, $\delta$-perturbation

Eremin D.A., Ivanov D.A., Popov Igor: Regular Potential Approximation for $\delta$-Perturbation Supported by Curve of the Laplace-Beltrami Operator on the Sphere. Z. Anal. Anwend. 31 (2012), 125-137. doi: 10.4171/ZAA/1451