On a class of translation-invariant spaces of quasianalytic ultradistributions
- Author
- Pavel Dimovski, Bojan Prangoski and Jasson Vindas Diaz (UGent)
- Organization
- Project
- Abstract
- A class of translation-invariant Banach spaces of quasianalytic ultradistributions is introduced and studied. They are Banach modules over a Beurling algebra. Based on this class of Banach spaces, we define corresponding test function spaces $\mathcal{D}^*_E$ and their strong duals $\mathcal{D}'^*_{E'_{\ast}}$ of quasianalytic type, and study convolution and multiplicative products on $\mathcal{D}'^*_{E'_{\ast}}$. These new spaces generalize previous works about translation-invariant spaces of tempered (non-quasianalytic ultra-) distributions; in particular, our new considerations apply to the settings of Fourier hyperfunctions and ultrahyperfunctions. New weighted $\mathcal{D}'^{\ast}_{L^{p}_{\eta}}$ spaces of quasianalytic ultradistributions are analyzed.
- Keywords
- Tempered ultradistributions, Hyperfunctions, Translation-invariant Banach space of ultradistributions, Beurling algebra, Quasianalytic ultradistributions, Convolution of ultradistributions
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Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-6967941
- MLA
- Dimovski, Pavel, et al. “On a Class of Translation-Invariant Spaces of Quasianalytic Ultradistributions.” NOVI SAD JOURNAL OF MATHEMATICS, edited by Jelena Aleksić et al., vol. 45, no. 1, 2015, pp. 143–75.
- APA
- Dimovski, P., Prangoski, B., & Vindas Diaz, J. (2015). On a class of translation-invariant spaces of quasianalytic ultradistributions. NOVI SAD JOURNAL OF MATHEMATICS, 45(1), 143–175.
- Chicago author-date
- Dimovski, Pavel, Bojan Prangoski, and Jasson Vindas Diaz. 2015. “On a Class of Translation-Invariant Spaces of Quasianalytic Ultradistributions.” Edited by Jelena Aleksić, Michael Kunzinger, and Nenad Teofanov. NOVI SAD JOURNAL OF MATHEMATICS 45 (1): 143–75.
- Chicago author-date (all authors)
- Dimovski, Pavel, Bojan Prangoski, and Jasson Vindas Diaz. 2015. “On a Class of Translation-Invariant Spaces of Quasianalytic Ultradistributions.” Ed by. Jelena Aleksić, Michael Kunzinger, and Nenad Teofanov. NOVI SAD JOURNAL OF MATHEMATICS 45 (1): 143–175.
- Vancouver
- 1.Dimovski P, Prangoski B, Vindas Diaz J. On a class of translation-invariant spaces of quasianalytic ultradistributions. Aleksić J, Kunzinger M, Teofanov N, editors. NOVI SAD JOURNAL OF MATHEMATICS. 2015;45(1):143–75.
- IEEE
- [1]P. Dimovski, B. Prangoski, and J. Vindas Diaz, “On a class of translation-invariant spaces of quasianalytic ultradistributions,” NOVI SAD JOURNAL OF MATHEMATICS, vol. 45, no. 1, pp. 143–175, 2015.
@article{6967941,
abstract = {{A class of translation-invariant Banach spaces of quasianalytic ultradistributions is introduced and studied. They are Banach modules over a Beurling algebra. Based on this class of Banach spaces, we define corresponding test function spaces $\mathcal{D}^*_E$ and their strong duals $\mathcal{D}'^*_{E'_{\ast}}$ of quasianalytic type, and study convolution and multiplicative products on $\mathcal{D}'^*_{E'_{\ast}}$. These new spaces generalize previous works about translation-invariant spaces of tempered (non-quasianalytic ultra-) distributions; in particular, our new considerations apply to the settings of Fourier hyperfunctions and ultrahyperfunctions. New weighted $\mathcal{D}'^{\ast}_{L^{p}_{\eta}}$ spaces of quasianalytic ultradistributions are analyzed.}},
author = {{Dimovski, Pavel and Prangoski, Bojan and Vindas Diaz, Jasson}},
editor = {{Aleksić, Jelena and Kunzinger, Michael and Teofanov, Nenad}},
issn = {{1450-5444}},
journal = {{NOVI SAD JOURNAL OF MATHEMATICS}},
keywords = {{Tempered ultradistributions,Hyperfunctions,Translation-invariant Banach space of ultradistributions,Beurling algebra,Quasianalytic ultradistributions,Convolution of ultradistributions}},
language = {{eng}},
number = {{1}},
pages = {{143--175}},
title = {{On a class of translation-invariant spaces of quasianalytic ultradistributions}},
url = {{http://www.dmi.uns.ac.rs/nsjom/Papers/45_1/NSJOM_45_1_143_175.pdf}},
volume = {{45}},
year = {{2015}},
}