Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type
Muratbekov M. Muratbekov M. Igissinov S.
November 2023Multidisciplinary Digital Publishing Institute (MDPI)
Mathematics
2023#11Issue 22
In this paper, we study a differential operator of parabolic type with a variable and unbounded coefficient, defined on an infinite strip. Sufficient conditions for the existence and compactness of the resolvent are established, and an estimate for the maximum regularity of solutions of the equation (Formula presented.) is obtained. Two-sided estimates for the distribution function of approximation numbers are obtained. As is known, estimates of approximation numbers show the rate of best approximation of the resolvent of an operator by finite-dimensional operators. The paper proves the assertion about the existence of positive eigenvalues among the eigenvalues of the given operator and finds two-sided estimates for them.
a singular numbers , an eigenvalues , an unbounded domain , parabolic type operator , separability
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Department of Mathematics, M.Kh.Dulaty Taraz Regional University, Taraz, 080000, Kazakhstan
Distance Learning Center, Esil University, Astana, 010000, Kazakhstan
Department of Mathematics
Distance Learning Center
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