Journal of Operator Theory

Volume 43, Issue 2, Spring 2000 pp. 243-262.

Pseudospectra of differential operators

Authors: E. Brian Davies
Author institution: Department of Mathematics, King's College, Strand, London WC2R 2LS, England

Summary: We study the pseudospectral theory of a variety of non-self-adjoint constant coefficient and variable coefficient differential operators, showing that the phenomenon of non-trivial pseudospectra is typical rather than exceptional. We prove that the pseudospectra provide more stable information about the operators under various limiting procedures than does the spectrum.

Keywords: Spectrum, pseudospectrum, norms of inverses, resolvent operators, differential operators

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