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Ukrainian Mathematical Journal

, Volume 69, Issue 10, pp 1607–1630 | Cite as

B-Coercive Convolution Equations in Weighted Function Spaces and Their Applications

  • H. K. Musaev
  • V. B. Shakhmurov
Article
  • 26 Downloads

We study the properties of B-separability for elliptic convolution operators in weighted Besov spaces and establish sharp estimates for the resolvents of the convolution operators. As a result, it is shown that these operators are positive and, in addition, play the role of negative generators of analytic semigroups. Moreover, the maximal B-regularity properties are established for the Cauchy problem for a parabolic convolution equation. Finally, these results are applied to obtain the maximal regularity properties for anisotropic integrodifferential equations and a system of infinitely many convolution equations.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • H. K. Musaev
    • 1
  • V. B. Shakhmurov
    • 2
  1. 1.Baku State UniversityBakuAzerbaijan
  2. 2.Okan UniversityIstanbulTurkey

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