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On the inclusion relations between Gelfand–Shilov spaces

Andreas Debrouwere, Lenny Neyt (UGent) and Jasson Vindas Diaz (UGent)
(2025) STUDIA MATHEMATICA. 283. p.237-256
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Abstract
We study inclusion relations between Gelfand–Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included in one another in terms of growth relations for the defining weight sequence and weight function systems. Our general framework allows for a unified treatment of the Gelfand–Shilov spaces S[M][A] (defined via weight sequences M and A) and the Beurling–Björck spaces S[ω][η] (defined via weight functions ω and η).
Keywords
Gelfand-Shilov spaces, inclusion relations, weight sequence systems, weight function systems, ultradifferentiable functions, Beurling-Björck spaces, OPERATORS

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Citation

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MLA
Debrouwere, Andreas, et al. “On the Inclusion Relations between Gelfand–Shilov Spaces.” STUDIA MATHEMATICA, vol. 283, 2025, pp. 237–56, doi:10.4064/sm240708-15-2.
APA
Debrouwere, A., Neyt, L., & Vindas Diaz, J. (2025). On the inclusion relations between Gelfand–Shilov spaces. STUDIA MATHEMATICA, 283, 237–256. https://doi.org/10.4064/sm240708-15-2
Chicago author-date
Debrouwere, Andreas, Lenny Neyt, and Jasson Vindas Diaz. 2025. “On the Inclusion Relations between Gelfand–Shilov Spaces.” STUDIA MATHEMATICA 283: 237–56. https://doi.org/10.4064/sm240708-15-2.
Chicago author-date (all authors)
Debrouwere, Andreas, Lenny Neyt, and Jasson Vindas Diaz. 2025. “On the Inclusion Relations between Gelfand–Shilov Spaces.” STUDIA MATHEMATICA 283: 237–256. doi:10.4064/sm240708-15-2.
Vancouver
1.
Debrouwere A, Neyt L, Vindas Diaz J. On the inclusion relations between Gelfand–Shilov spaces. STUDIA MATHEMATICA. 2025;283:237–56.
IEEE
[1]
A. Debrouwere, L. Neyt, and J. Vindas Diaz, “On the inclusion relations between Gelfand–Shilov spaces,” STUDIA MATHEMATICA, vol. 283, pp. 237–256, 2025.
@article{01K6WCBVBAQPP8EZXNPFSEC0XB,
  abstract     = {{We study inclusion relations between Gelfand–Shilov type spaces defined via a weight (multi-)sequence system, a weight function system, and a translation-invariant Banach function space. We characterize when such spaces are included in one another in terms of growth relations for the defining weight sequence and weight function systems. Our general framework allows for a unified treatment of the Gelfand–Shilov spaces S[M][A] (defined via weight sequences M and A) and the Beurling–Björck spaces S[ω][η] (defined via weight functions ω and η).}},
  author       = {{Debrouwere, Andreas and Neyt, Lenny and Vindas Diaz, Jasson}},
  issn         = {{0039-3223}},
  journal      = {{STUDIA MATHEMATICA}},
  keywords     = {{Gelfand-Shilov spaces,inclusion relations,weight sequence systems,weight function systems,ultradifferentiable functions,Beurling-Björck spaces,OPERATORS}},
  language     = {{eng}},
  pages        = {{237--256}},
  title        = {{On the inclusion relations between Gelfand–Shilov spaces}},
  url          = {{http://doi.org/10.4064/sm240708-15-2}},
  volume       = {{283}},
  year         = {{2025}},
}
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