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Translation-modulation invariant Banach spaces of ultradistributions

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Abstract
We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener-Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions M-F on R-d, associated to translation-modulation invariant Banach spaces of ultradistributions F on R-2d.
Keywords
Ultradistributions, Modulation spaces, Gelfand-Shilov spaces, Translation-invariant Banach space, Translation-modulation invariant Banach spaces of ultradistributions

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MLA
Dimovski, Pavel, et al. “Translation-Modulation Invariant Banach Spaces of Ultradistributions.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, no. 3, 2019, pp. 819–41, doi:10.1007/s00041-018-9610-x.
APA
Dimovski, P., Pilipović, S., Prangoski, B., & Vindas Diaz, J. (2019). Translation-modulation invariant Banach spaces of ultradistributions. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 25(3), 819–841. https://doi.org/10.1007/s00041-018-9610-x
Chicago author-date
Dimovski, Pavel, Stevan Pilipović, Bojan Prangoski, and Jasson Vindas Diaz. 2019. “Translation-Modulation Invariant Banach Spaces of Ultradistributions.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25 (3): 819–41. https://doi.org/10.1007/s00041-018-9610-x.
Chicago author-date (all authors)
Dimovski, Pavel, Stevan Pilipović, Bojan Prangoski, and Jasson Vindas Diaz. 2019. “Translation-Modulation Invariant Banach Spaces of Ultradistributions.” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 25 (3): 819–841. doi:10.1007/s00041-018-9610-x.
Vancouver
1.
Dimovski P, Pilipović S, Prangoski B, Vindas Diaz J. Translation-modulation invariant Banach spaces of ultradistributions. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. 2019;25(3):819–41.
IEEE
[1]
P. Dimovski, S. Pilipović, B. Prangoski, and J. Vindas Diaz, “Translation-modulation invariant Banach spaces of ultradistributions,” JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol. 25, no. 3, pp. 819–841, 2019.
@article{8584927,
  abstract     = {{We introduce and study a new class of translation-modulation invariant Banach spaces of ultradistributions. These spaces show stability under Fourier transform and tensor products; furthermore, they have a natural Banach convolution module structure over a certain associated Beurling algebra, as well as a Banach multiplication module structure over an associated Wiener-Beurling algebra. We also investigate a new class of modulation spaces, the Banach spaces of ultradistributions M-F on R-d, associated to translation-modulation invariant Banach spaces of ultradistributions F on R-2d.}},
  author       = {{Dimovski, Pavel and Pilipović, Stevan and Prangoski, Bojan and Vindas Diaz, Jasson}},
  issn         = {{1069-5869}},
  journal      = {{JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS}},
  keywords     = {{Ultradistributions,Modulation spaces,Gelfand-Shilov spaces,Translation-invariant Banach space,Translation-modulation invariant Banach spaces of ultradistributions}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{819--841}},
  title        = {{Translation-modulation invariant Banach spaces of ultradistributions}},
  url          = {{http://dx.doi.org/10.1007/s00041-018-9610-x}},
  volume       = {{25}},
  year         = {{2019}},
}

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