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Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type

Author

Listed:
  • Mussakan Muratbekov

    (Department of Mathematics, M.Kh.Dulaty Taraz Regional University, Taraz 080000, Kazakhstan
    These authors contributed equally to this work.)

  • Madi Muratbekov

    (Distance Learning Center, Esil University, Astana 010000, Kazakhstan
    These authors contributed equally to this work.)

  • Sabit Igissinov

    (Department of Mathematics, M.Kh.Dulaty Taraz Regional University, Taraz 080000, Kazakhstan
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Mussakan Muratbekov & Madi Muratbekov & Sabit Igissinov, 2023. "Estimates for the Approximation and Eigenvalues of the Resolvent of a Class of Singular Operators of Parabolic Type," Mathematics, MDPI, vol. 11(22), pages 1-13, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:22:p:4584-:d:1276691
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