On closability and bounded invertibility of mixed type differential operator in an unbounded domain

Authors

  • M.B. Muratbekov
  • S.Zh. Igisinov

Keywords:

operator of mixed type, closure, resolvent, bounded invertibility, inverse operator, unbounded domain, strip, covering, kernel, conjugate operator, Fourier transform

Abstract

In this paper we consider a class of mixed type singular differential operator in an unbounded domain. Initially closability of the operator is proved. Because there is no a priori estimate, which exists in the case of an operator whose coefficients depend only on the variable y in front of terms ux (x, y) and u (x, y). The existence of the resolvent of the operator in an unbounded domain is proved. The method of localization and methods of the theory of linear operators are used.

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Published

2015-06-29

How to Cite

Muratbekov, M., & Igisinov, S. (2015). On closability and bounded invertibility of mixed type differential operator in an unbounded domain. Bulletin of the Karaganda University. Mathematics Series, 78(2), 106–112. Retrieved from http://mts.buketov.edu.kz/index.php/mathematics-vestnik/article/view/30

Issue

2015 (78) 2

Section

MATHEMATICS