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1997 Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators
Ralph Delaubenfels, Yansong Lei
Abstr. Appl. Anal. 2(1-2): 121-136 (1997). DOI: 10.1155/S1085337597000304


Let iAj(1jn) be generators of commuting bounded strongly continuous groups, A(A1,A2,,An). We show that, when f has sufficiently many polynomially bounded derivatives, then there exist k,r>0 such that f(A) has a (1+|A|2)r-regularized BCk(f(Rn)) functional calculus. This immediately produces regularized semigroups and cosine functions with an explicit representation; in particular, when f(Rn)R, then, for appropriate k,r, t(1it)keitf(A)(1+|A|2)r is a Fourier-Stieltjes transform, and when f(Rn)[0,), then t(1+t)ketf(A)(1+|A|2)r is a Laplace-Stieltjes transform. With Ai(D1,,Dn),f(A) is a pseudodifferential operator on Lp(Rn)(1p<) or BUC(Rn).


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Ralph Delaubenfels. Yansong Lei. "Regularized functional calculi, semigroups, and cosine functions for pseudodifferential operators." Abstr. Appl. Anal. 2 (1-2) 121 - 136, 1997.


Published: 1997
First available in Project Euclid: 7 April 2003

zbMATH: 0937.47015
MathSciNet: MR1604169
Digital Object Identifier: 10.1155/S1085337597000304

Primary: 47A60
Secondary: 47D03 , 47D06 , 47D09 , 47F05

Keywords: cosine functions , pseudodifferential operators , Regularized functional calculi , semigroups

Rights: Copyright © 1997 Hindawi

Vol.2 • No. 1-2 • 1997
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