ON THE MINIMALITY OF SYSTEMS OF ROOT FUNCTIONS OF THE LAPLACE OPERATOR IN THE PUNCTURED DOMAIN

Авторы

  • B. Bekbolat Al–Farabi Kazakh National University, Almaty, Kazakhstan
  • D. B. Nurakhmetov S.Seifullin Kazakh Agro Technical University, Astana, Kazakhstan
  • N. Tokmagambetov Ghent University, Ghent, Belgium
  • G. H. Aimal Rasa Al–Farabi Kazakh National University, Almaty, Kazakhstan

Ключевые слова:

Laplace operator, punctured domain, resolvent, meromorphic function, correctly solvable boundary value problems, root functions system, minimal system.

Аннотация

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.

Загрузки

Опубликован

2019-08-10

Как цитировать

B. Bekbolat, D. B. Nurakhmetov, N. Tokmagambetov, & G. H. Aimal Rasa. (2019). ON THE MINIMALITY OF SYSTEMS OF ROOT FUNCTIONS OF THE LAPLACE OPERATOR IN THE PUNCTURED DOMAIN. Известия НАН РК. Серия физико-математическая, (4), 92–109. извлечено от http://189185.vm7pq.group/physics-mathematics/article/view/1680

Выпуск

№ 4 (2019): Известия НАН РК. Серия физико-математическая

Раздел

Статьи