On the regularization of sequences and associated weight functions
Abstract
We revisit and generalize the geometric procedure of regularizing a sequence of real numbers with respect to a so-called regularizing function. This approach was studied by S. Mandelbrojt and becomes useful and necessary when working with corresponding classes of ultradifferentiable functions defined via weight sequences and analogous weighted spaces. In this note we also study non-standard situations for the construction yielding the (log-)convex minorant of a sequence and allow a "blow-up" for the regularizing function.
Cite
@article{arxiv.2307.07902,
title = {On the regularization of sequences and associated weight functions},
author = {Gerhard Schindl},
journal= {arXiv preprint arXiv:2307.07902},
year = {2024}
}
Comments
30 pages; this version is accepted for publ. in the Bull. Belg. Math. Soc. - Simon Stevin. According to the comments made by the anonymous referee we have rewritten the introduction and improved the presentation of the main results; some stylistic minor changes have been applied