Local spectral properties of generators of C-0-groups and Bernstein type inequalities


Mustafayev H., Temel C.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.357, no.1, pp.273-283, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 357 Issue: 1
  • Publication Date: 2009
  • Doi Number: 10.1016/j.jmaa.2009.04.017
  • Journal Name: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.273-283

Abstract

Let T = {T(t)}(t epsilon R) be a C-0-group on a complex Banach space X dominated by a weight function omega(t) = (1 + vertical bar t vertical bar)(alpha) (0 <= alpha < 1) and let A be its generator with domain D(A). Among other things, it is shown that if the operator A has compact local spectrum at x is an element of X, then x is an element of D(A) and there exist double sequences of real numbers and (t(n))(n epsilon Z) Such that