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Invariance of the ${L_p}$ Spectrum for Hypoelliptic Operators

Author(s): Hans-Gerd Leopold; Elmar Schrohe
Journal: Proc. Amer. Math. Soc. 125 (1997), 3679-3687.
MSC (1991): Primary 35P05, 35H05, 47G30
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Abstract: We show that the spectra of the $L_p$-realizations for a class of hypoelliptic (pseudo-)differential operators are independent of $p$ in an interval around $p=2$ depending on the growth properties of the symbol. For elliptic operators we obtain the classical boundedness interval of Fefferman; in the general case we obtain a smaller interval which is as large as one can possibly expect it to be.

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Additional Information:

Hans-Gerd Leopold
Affiliation: Mathematisches Institut, Fakultät für Mathematik und Informatik, Friedrich- Schiller-Universität Jena, D-07740 Jena, Germany
Email: leopold@minet.uni-jena.de

Elmar Schrohe
Affiliation: Max-Planck-Arbeitsgruppe ``Partielle Differentialgleichungen und Komplexe Ana- lysis'', Universität Potsdam, D-14415 Potsdam, Germany
Email: schrohe@mpg-ana.uni-potsdam.de

DOI: 10.1090/S0002-9939-97-04123-3
PII: S 0002-9939(97)04123-3
Keywords: $L_p$-spectrum, spectral independence, hypoelliptic pseudodifferential operators
Received by editor(s): July 29, 1996
Additional Notes: The first author was supported in part by DFG-contract Tr 374/1-1
Communicated by: Palle E. T. Jorgensen
Copyright of article: Copyright 1997, American Mathematical Society

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