Continuity of Translation Operators

Details Continuity of Translation Operators Continuity of Translation Operators

2010-10-31

arxiv.org/abs/1011.0212v1

Mathematics

Classical Analysis and ODEs

to appear, PAMS

Scientific paper

For a Radon measure $\mu$ on $\bbR,$ we show that $L^{\infty}(\mu)$ is invariant under the group of translation operators $T_t(f)(x) = {$f(x-t)$}\ (t \in \bbR)$ if and only if $\mu$ is equivalent to Lebesgue measure $m$. We also give necessary and sufficient conditions for $L^p(\mu),\1 \leq p < \infty,$ to be invariant under the group $\{T_t\}$ in terms of the Radon-Nikodym derivative w.r.t. $m$.

Affiliated with

Also associated with

No associations

Rating

Continuity of Translation Operators does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Continuity of Translation Operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Continuity of Translation Operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-441555