Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418991 | Journal of Mathematical Analysis and Applications | 2013 | 10 Pages |
Abstract
For semigroups S=R+,Z+ and Z+k, we show that if T is a representation of S by contractions on a Hilbert space then inftâSâT(t)fÌ(T)â=sup{|f(λ)|,λâSpu(T,S)}, where fâL1(S) and Spu(T,S) is the unitary spectrum of T with respect to S. For T a representation of a suitable semigroup S by contractions on a Banach space, we give sharp conditions on Spu(T,S) which guarantee that the equality above holds. These conditions concern the thinness of Spu(T,S) in the harmonic analysis sense. These results are related to theorems of Katznelson-Tzafriri type, which give conditions guaranteeing that inftâSâT(t)fÌ(T)â vanishes.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mohamed Zarrabi,