Journal
MATHEMATISCHE NACHRICHTEN
Volume 279, Issue 3, Pages 319-326Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.200310363
Keywords
M-ellipticity; minimal and maximal pseudo-differential operators; spectrum; essential spectrum
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We construct the minimal and maximal extensions in L-p (R-n), 1 < p < infinity, for M-elliptic pseudo-differential operators initiated by Garello and Morando. We prove that they are equal and determine the domains of the minimal, and hence maximal, extensions of M-elliptic pseudo-differential operators. For M-elliptic pseudo-differential operators with constant coefficients, the spectra and essential spectra are computed. An application to quantization is given. (c) 2006 WILEY VCH Verlag GmbH & Co. KGaA, Weinheim.
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