L p Spectral Independence of Elliptic Operators via Commutator Estimates

L p Spectral Independence of Elliptic Operators via Commutator Estimates Let {T p:q 1⩽ p⩽ q 2} be a family of consistent C 0 semigroups on L p(Ω), with q 1,q 2 ∈ [1,∞) and Ω ⫅ ℝ open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p ∈ [q 1,q 2. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

L p Spectral Independence of Elliptic Operators via Commutator Estimates

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1999 by Kluwer Academic Publishers
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009777826708
Publisher site
See Article on Publisher Site

Abstract

Let {T p:q 1⩽ p⩽ q 2} be a family of consistent C 0 semigroups on L p(Ω), with q 1,q 2 ∈ [1,∞) and Ω ⫅ ℝ open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p ∈ [q 1,q 2.

Journal

PositivitySpringer Journals

Published: Oct 16, 2004

References

  • Integral representations of resolvents and semigroups
    Arendt, W.; Bukhvalov, A. V.

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