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Volume 41, Issue 3
Separation of Sequences and Multipliers in the Space of Tempered Distributions

Ricardo Estrada & Kevin Kellinsky-Gonzalez

DOI: 10.4208/ata.OA-2024-0015

Anal. Theory Appl., 41 (2025), pp. 208-228.

Published online: 2025-09

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  • Abstract

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 $S'(\mathbb{R})$ and in other related spaces and the separation properties of the sequence of its zeros.
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.

  • Keywords

Tempered distributions, division problems, separation of sequences.

  • AMS Subject Headings

46F10

  • Copyright

COPYRIGHT: © Global Science Press

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  • BibTex
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  • TXT
@Article{ATA-41-208, author = {Estrada , Ricardo and Kellinsky-Gonzalez , Kevin}, title = {Separation of Sequences and Multipliers in the Space of Tempered Distributions}, journal = {Analysis in Theory and Applications}, year = {2025}, volume = {41}, number = {3}, pages = {208--228}, abstract = {

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 $S'(\mathbb{R})$ and in other related spaces and the separation properties of the sequence of its zeros.
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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2024-0015}, url = {http://global-sci.org/intro/article_detail/ata/24480.html} }
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 -

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 $S'(\mathbb{R})$ and in other related spaces and the separation properties of the sequence of its zeros.
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.

Estrada , Ricardo and Kellinsky-Gonzalez , Kevin. (2025). Separation of Sequences and Multipliers in the Space of Tempered Distributions. Analysis in Theory and Applications. 41 (3). 208-228. doi:10.4208/ata.OA-2024-0015
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