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Convolution of ultradistributions and ultradistribution spaces associated to translation-invariant Banach spaces

(2016) KYOTO JOURNAL OF MATHEMATICS. 56(2). p.401-440
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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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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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