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Functional calculi and decomposability of unbounded multiplier operators in LP(ℝN)

Published online by Cambridge University Press:  20 January 2009

Ernst Albrecht  and
Werner J. Ricker
Ernst Albrecht
Affiliation:
Fachbereich MathematikUniversität des SaarlandesPostfach 1150D-66141 Saarbrücken, Germany
Werner J. Ricker
Affiliation:
School of MathematicsUniversity of New South WalesP.O. Box 1Kensington, N.W.S., 2033, Australia
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Abstract

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It is known, for each 1<p<∞, p≠2, that there exist differential operators in LP(ℝN) which are not (unbounded) decomposable operators in the sense of C. Foiaş. In this note we exhibit large classes of differential (and unbounded multiplier operators which are decomposable in LP(ℝN) and hence have good spectral mapping properties; the arguments are based on the existence of a sufficiently rich functional calculus. The basic idea is to take advantage of existing classical results on p-multipliers and use them to generate appropriate functional calculi.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 151 - 166
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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