New distribution spaces associated to translation-invariant Banach spaces
- Author
- Pavel Dimovski, Stevan Pilipović and Jasson Vindas Diaz (UGent)
- Organization
- Project
- Abstract
- We introduce and study new distribution spaces, the test function space $\mathcal{D}_E$ and its strong dual $\mathcal{D}'_{E'_{\ast}}$. These spaces generalize the Schwartz spaces $\mathcal{D}_{L^{q}}$, $\mathcal{D}'_{L^{p}}$, $\mathcal{B}'$ and their weighted versions. The construction of our new distribution spaces is based on the analysis of a suitable translation-invariant Banach space of distributions $E$, which turns out to be a convolution module over a Beurling algebra $L^{1}_{\omega}$. The Banach space $E'_{\ast}$ stands for $L_{\check{\omega}}^1\ast E'$. We also study convolution and multiplicative products on $\mathcal{D}'_{E'_{\ast}}$.
- Keywords
- Beurling algebras, L-p and D '(Lp) weighted spaces, Convolution of distributions, Translation-invariant Banach spaces of tempered distributions, CALCULUS APPROACH, Schwartz distributions, HYPERFUNCTIONS, ALGEBRAS
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-6968453
- MLA
- Dimovski, Pavel, et al. “New Distribution Spaces Associated to Translation-Invariant Banach Spaces.” MONATSHEFTE FUR MATHEMATIK, vol. 177, no. 4, 2015, pp. 495–515, doi:10.1007/s00605-014-0706-3.
- APA
- Dimovski, P., Pilipović, S., & Vindas Diaz, J. (2015). New distribution spaces associated to translation-invariant Banach spaces. MONATSHEFTE FUR MATHEMATIK, 177(4), 495–515. https://doi.org/10.1007/s00605-014-0706-3
- Chicago author-date
- Dimovski, Pavel, Stevan Pilipović, and Jasson Vindas Diaz. 2015. “New Distribution Spaces Associated to Translation-Invariant Banach Spaces.” MONATSHEFTE FUR MATHEMATIK 177 (4): 495–515. https://doi.org/10.1007/s00605-014-0706-3.
- Chicago author-date (all authors)
- Dimovski, Pavel, Stevan Pilipović, and Jasson Vindas Diaz. 2015. “New Distribution Spaces Associated to Translation-Invariant Banach Spaces.” MONATSHEFTE FUR MATHEMATIK 177 (4): 495–515. doi:10.1007/s00605-014-0706-3.
- Vancouver
- 1.Dimovski P, Pilipović S, Vindas Diaz J. New distribution spaces associated to translation-invariant Banach spaces. MONATSHEFTE FUR MATHEMATIK. 2015;177(4):495–515.
- IEEE
- [1]P. Dimovski, S. Pilipović, and J. Vindas Diaz, “New distribution spaces associated to translation-invariant Banach spaces,” MONATSHEFTE FUR MATHEMATIK, vol. 177, no. 4, pp. 495–515, 2015.
@article{6968453,
abstract = {{We introduce and study new distribution spaces, the test function space $\mathcal{D}_E$ and its strong dual $\mathcal{D}'_{E'_{\ast}}$. These spaces generalize the Schwartz spaces $\mathcal{D}_{L^{q}}$, $\mathcal{D}'_{L^{p}}$, $\mathcal{B}'$ and their weighted versions. The construction of our new distribution spaces is based on the analysis of a suitable translation-invariant Banach space of distributions $E$, which turns out to be a convolution module over a Beurling algebra $L^{1}_{\omega}$. The Banach space $E'_{\ast}$ stands for $L_{\check{\omega}}^1\ast E'$. We also study convolution and multiplicative products on $\mathcal{D}'_{E'_{\ast}}$.}},
author = {{Dimovski, Pavel and Pilipović, Stevan and Vindas Diaz, Jasson}},
issn = {{0026-9255}},
journal = {{MONATSHEFTE FUR MATHEMATIK}},
keywords = {{Beurling algebras,L-p and D '(Lp) weighted spaces,Convolution of distributions,Translation-invariant Banach spaces of tempered distributions,CALCULUS APPROACH,Schwartz distributions,HYPERFUNCTIONS,ALGEBRAS}},
language = {{eng}},
number = {{4}},
pages = {{495--515}},
title = {{New distribution spaces associated to translation-invariant Banach spaces}},
url = {{http://dx.doi.org/10.1007/s00605-014-0706-3}},
volume = {{177}},
year = {{2015}},
}
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