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Differential Equations

, Volume 46, Issue 2, pp 214–223 | Cite as

Finite-difference operators in the study of differential operators: Solution estimates

  • A. G. Baskakov
  • Yu. N. Sintyaev
Partial Differential Equations

Abstract

The main results of the present paper are related to the use of finite-difference operators for estimating the norms of inverses of differential operators with unbounded operator coefficients. We obtain a new proof of the Gearhart-Prüss spectral mapping theorem for operator semigroups in a Hilbert space and estimate the exponential dichotomy exponents of an operator semigroup.

Keywords

Hilbert Space Banach Space Differential Operator Inverse Operator Unbounded Operator 
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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • A. G. Baskakov
    • 1
  • Yu. N. Sintyaev
    • 1
  1. 1.Voronezh State UniversityVoronezhRussia

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