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# New distribution spaces associated to translation-invariant Banach spaces

(2015) 177(4). p.495-515
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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

MLA
Dimovski, Pavel, Stevan Pilipović, and Jasson Vindas Diaz. “New Distribution Spaces Associated to Translation-invariant Banach Spaces.” MONATSHEFTE FUR MATHEMATIK 177.4 (2015): 495–515. Print.
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.
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.
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.
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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