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- Title
Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type.
- Authors
Muratbekov, Mussakan; Muratbekov, Madi; Igissinov, Sabit
- 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 L u = 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.
- Subjects
PARABOLIC operators; EIGENVALUES; DISTRIBUTION (Probability theory); DIFFERENTIAL operators; RESOLVENTS (Mathematics); CARLEMAN theorem
- Publication
Mathematics (2227-7390), 2023, Vol 11, Issue 22, p4584
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math11224584