Journal article

THE a-DRAZIN INVERSE AND ERGODIC BEHAVIOUR OF SEMIGROUPS AND COSINE OPERATOR FUNCTIONS

PL Butzer, JJ Koliha

JOURNAL OF OPERATOR THEORY | THETA FOUNDATION | Published : 2009

Abstract

The paper introduces a special type of a Drazin-like inverse for closed linear operators that arises naturally in ergodic theory of operator semigroups and cosine operator functions. The Drazin inverse for closed linear operators defined by Nashed and Zhao and in a more general form by Koliha and Tran is not sufficiently general to be applicable to operator semigroups. The a-Drazin inverse is in general a closed, not necessarily bounded, operator. The paper gives applications of the inverse to partial differential equations. © Copyright by THETA, 2009.

University of Melbourne Researchers

Grants

Awarded by University of Melbourne


Funding Acknowledgements

This research project was partially supported by a grant from the Graduiertenkolleg "Hierarchie und Symmetrie in mathematischen Modellen", RWTH, Aachen. The second author was partially supported by the University of Melbourne Grant MRDGS 425007.