TY - JOUR
T1 - Separation of Sequences and Multipliers in the Space of Tempered Distributions
AU - Estrada , Ricardo
AU - Kellinsky-Gonzalez , Kevin
JO - Analysis in Theory and Applications
VL - 3
SP - 208
EP - 228
PY - 2025
DA - 2025/09
SN - 41
DO - http://doi.org/10.4208/ata.OA-2024-0015
UR - https://global-sci.org/intro/article_detail/ata/24480.html
KW - Tempered distributions, division problems, separation of sequences.
AB - <p style="text-align: justify;">We consider the notions of $v$-separation and $(N,v)$-separation for increasing
 sequences that tend to infinity. We study several of the connections between the properties of a multiplier in the space $S&#39;(\mathbb{R})$ and in other related spaces and the separation
 properties of the sequence of its zeros.<br/>We also prove that a distributional division problem $$Fh=f,$$always has tempered solutions $h$ for any tempered data $f$ if and only if the non integrable function $1/F$ admits regularizations that are tempered, and that this holds if
 and only if the pseudofunction $\mathcal{P} f (1/F)$ is tempered.</p>