Translation beyond Delsarte
Classical Analysis and ODEs
2023-06-16 v2
Abstract
We introduce general translations as solutions to Cauchy or Dirichlet problems. This point of view allows us to handle the heat-diffusion semigroup as a translation. With the given examples Kolmogorov-Riesz characterization of compact sets in certain spaces are given. Pego-type characterizations are also derived. Finally for some examples the equivalence of the corresponding modulus of smoothness and K-functional is pointed out.
Keywords
Cite
@article{arxiv.2207.00359,
title = {Translation beyond Delsarte},
author = {Á. P. Horváth},
journal= {arXiv preprint arXiv:2207.00359},
year = {2023}
}
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23 pages