Proceedings of the American Mathematical Society

Author(s): Patrick J. Rabier
Journal: Proc. Amer. Math. Soc. 135 (2007), 3875-3885.
MSC (2000): Primary 47A53, 47F05, 35J45
Posted: August 29, 2007
Retrieve article in: PDF

Abstract: If $P(x,\partial )$ is an $r\times r$ system of differential operators on $\mathbb{R}^{N}$ having continuous coefficients with vanishing oscillation at infinity, the Cordes-Illner theory ensures that $P(x,\partial )$ is Fredholm from $(W^{m,p})^{r}$ to $(L^{p})^{r}$ for all or no value $p\in (1,\infty ).$ We prove that both the index (when defined) and the spectrum of $P(x,\partial )$ are independent of

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47A53, 47F05, 35J45

Patrick J. Rabier
Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
Email: rabier@imap.pitt.edu

DOI: 10.1090/S0002-9939-07-08896-X
PII: S 0002-9939(07)08896-X
Keywords: Fredholm operator, index, differential operator, system, spectrum.
Received by editor(s): January 14, 2006
Received by editor(s) in revised form: August 27, 2006
Posted: August 29, 2007
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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