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HEAT KERNEL ESTIMATES AND LP SPECTRAL INDEPENDENCE OF ELLIPTIC OPERATORS

Published online by Cambridge University Press:  01 May 1999

PEER CHRISTIAN KUNSTMANN
PEER CHRISTIAN KUNSTMANN
Affiliation:
Mathematisches Institut I, Universität Karlsruhe, Englerstr. 2, D–76128 Karlsruhe, Germany
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Abstract

Let Ω be an open subset of IRd, and let Tp for p∈[1, ∞) be consistent C0-semigroups given by kernels that satisfy an upper heat kernel estimate. Denoting their generators by Ap, we show that the spectrum σ(Ap) is independent of p∈[1, ∞). We also treat the case of weighted Lp-spaces for weights that satisfy a subexponential growth condition. An example shows that independence of the spectrum may fail for an exponential weight.

Type
NOTES AND PAPERS
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 3 , May 1999 , pp. 345 - 353
Copyright
© The London Mathematical Society 1999

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