Journal of Operator Theory

Volume 35, Issue 1, Winter 1996 pp. 3-37.

Local spectral properties of certain matrix differential operators in $L^p(\mathbbR^N)^m$

Authors: E. Albrecht (1) and W.J. Ricker (2)
Author institution:(1) Fachbereich Mathematik, Universität des Saarlandes, D-66041 Saarbrücken, GERMANY
(2) School of Mathematics, University of New South Wales, Sydney, NSW, 2052, AUSTRALIA

Summary: We investigate the local spectral behaviour of (constant coefficient) matrix differential operators, and more general matrix p-multiplier operators, in L^p-spaces (particularly, over $\mathbb R^N$). Of particular interest is the decomposability and spectral mapping properties of such operators, together with relevant functional calculi, when they are available.

Keywords: L^p-spaces, matrix p-multipliers, decomposability, functional calculi.

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