
Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces
- Author
- Pavel Dimovski, Stevan Pilipović, Bojan Prangoski and Jasson Vindas Diaz (UGent)
- Organization
- Project
- Abstract
- We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions. The spaces of convolutors O-C'*(R-d) for tempered ultradistributions are analyzed via the duality with respect to the test function spaces O-C*(R-d) introduced in this article. We also study ultradistribution spaces associated to translation-invariant Banach spaces of tempered ultradistributions and use their properties to provide a full characterization of the general convolution of Roumieu ultradistributions via the space of integrable ultradistributions. We show that the convolution of two Roumieu ultra distributions T, S is an element of D'({Mp}) (R-d) exists if and only if (phi * S)T is an element of D-L1'({Mp}) (R-d) for every phi is an element of D-{Mp} (R-d).
- Keywords
- Ultratempered convolutors, parametrix method, Beurling algebra, Convolution of ultradistributions, Translation-invariant Banach space of tempered ultradistributions
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Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8040391
- MLA
- Dimovski, Pavel, et al. “Convolution of Ultradistributions and Ultradistribution Spaces Associated to Translation-Invariant Banach Spaces.” KYOTO JOURNAL OF MATHEMATICS, vol. 56, no. 2, 2016, pp. 401–40, doi:10.1215/21562261-3478916.
- APA
- Dimovski, P., Pilipović, S., Prangoski, B., & Vindas Diaz, J. (2016). Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces. KYOTO JOURNAL OF MATHEMATICS, 56(2), 401–440. https://doi.org/10.1215/21562261-3478916
- Chicago author-date
- Dimovski, Pavel, Stevan Pilipović, Bojan Prangoski, and Jasson Vindas Diaz. 2016. “Convolution of Ultradistributions and Ultradistribution Spaces Associated to Translation-Invariant Banach Spaces.” KYOTO JOURNAL OF MATHEMATICS 56 (2): 401–40. https://doi.org/10.1215/21562261-3478916.
- Chicago author-date (all authors)
- Dimovski, Pavel, Stevan Pilipović, Bojan Prangoski, and Jasson Vindas Diaz. 2016. “Convolution of Ultradistributions and Ultradistribution Spaces Associated to Translation-Invariant Banach Spaces.” KYOTO JOURNAL OF MATHEMATICS 56 (2): 401–440. doi:10.1215/21562261-3478916.
- Vancouver
- 1.Dimovski P, Pilipović S, Prangoski B, Vindas Diaz J. Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces. KYOTO JOURNAL OF MATHEMATICS. 2016;56(2):401–40.
- IEEE
- [1]P. Dimovski, S. Pilipović, B. Prangoski, and J. Vindas Diaz, “Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces,” KYOTO JOURNAL OF MATHEMATICS, vol. 56, no. 2, pp. 401–440, 2016.
@article{8040391, abstract = {{We introduce and study a number of new spaces of ultradifferentiable functions and ultradistributions and we apply our results to the study of the convolution of ultradistributions. The spaces of convolutors O-C'*(R-d) for tempered ultradistributions are analyzed via the duality with respect to the test function spaces O-C*(R-d) introduced in this article. We also study ultradistribution spaces associated to translation-invariant Banach spaces of tempered ultradistributions and use their properties to provide a full characterization of the general convolution of Roumieu ultradistributions via the space of integrable ultradistributions. We show that the convolution of two Roumieu ultra distributions T, S is an element of D'({Mp}) (R-d) exists if and only if (phi * S)T is an element of D-L1'({Mp}) (R-d) for every phi is an element of D-{Mp} (R-d).}}, author = {{Dimovski, Pavel and Pilipović, Stevan and Prangoski, Bojan and Vindas Diaz, Jasson}}, issn = {{2156-2261}}, journal = {{KYOTO JOURNAL OF MATHEMATICS}}, keywords = {{Ultratempered convolutors,parametrix method,Beurling algebra,Convolution of ultradistributions,Translation-invariant Banach space of tempered ultradistributions}}, language = {{eng}}, number = {{2}}, pages = {{401--440}}, title = {{Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces}}, url = {{http://doi.org/10.1215/21562261-3478916}}, volume = {{56}}, year = {{2016}}, }
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