Muratbekov, M.; Muratbekov, M.; Igissinov, S. Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type. Mathematics2023, 11, 4584.
Muratbekov, M.; Muratbekov, M.; Igissinov, S. Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type. Mathematics 2023, 11, 4584.
Muratbekov, M.; Muratbekov, M.; Igissinov, S. Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type. Mathematics2023, 11, 4584.
Muratbekov, M.; Muratbekov, M.; Igissinov, S. Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type. Mathematics 2023, 11, 4584.
Abstract
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 Lu=f∈L_2(Ω) 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.
Keywords
parabolic type operator; an eigenvalues; a singular numbers; separability; an unbounded domain
Subject
Computer Science and Mathematics, Analysis
Copyright:
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