ON THE MINIMALITY OF SYSTEMS OF ROOT FUNCTIONS OF THE LAPLACE OPERATOR IN THE PUNCTURED DOMAIN - B. Bekbolat; D. B. Nurakhmetov; N. Tokmagambetov; G. H. Aimal Rasa (Academic Scientific Journal of Computer Science, 2019)
In this paper, we consider the Laplace operator in a punctured domain, which generates a class of “new” correctly solvable boundary value problems. And for this class of problems the resolvent formula is obtained. Also described are meromorphic functions that generate the root functions of the class of problems studied. The main goal is to study the minimality of root function systems. The paper is a continuation of [8], where a description is given of correctly solvable boundary value problems for the Laplace operator in punctured domains. The Laplace operator in the punctured domain, which generates the class of “new” correctly solvable boundary value problems, is considered, and the resolvent formula is obtained for the generated problems, and meromorphic functions are described that induce systems of functions. One of these systems is a system of eigenfunctions and associated functions. The last section is devoted to the study of the minimality of the system of root functions.