Advanced search
1 file | 335.28 KB Add to list

The nuclearity of Gelfand-Shilov spaces and kernel theorems

Andreas Debrouwere (UGent) , Lenny Neyt (UGent) and Jasson Vindas Diaz (UGent)
(2021) COLLECTANEA MATHEMATICA. 72(1). p.203-227
Author
Organization
Project
Abstract
We study the nuclearity of the Gelfand-Shilov spaces S(M)(W) and S{M}{W}, defined via a weight (multi-)sequence system M and a weight function system W. We obtain characterizations of nuclearity for these function spaces that are counterparts of those for Köthe sequence spaces. As an application, we prove new kernel theorems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces S(M)(A) and S{M}{A} (defined via weight sequences M and A) and the Beurling-Björck spaces S(ω)(η) and S{ω}{η} (defined via weight functions ω and η). Our results cover anisotropic cases as well.
Keywords
Applied Mathematics, General Mathematics, Gelfand-Shilov spaces, Nuclear spaces, Schwartz kernel theorems, Weight sequence systems, Weight function systems, PSEUDODIFFERENTIAL-OPERATORS

Downloads

  • 1910.09944.pdf
    • full text (Accepted manuscript)
    • |
    • open access
    • |
    • PDF
    • |
    • 335.28 KB

Citation

Please use this url to cite or link to this publication:

MLA
Debrouwere, Andreas, et al. “The Nuclearity of Gelfand-Shilov Spaces and Kernel Theorems.” COLLECTANEA MATHEMATICA, vol. 72, no. 1, 2021, pp. 203–27, doi:10.1007/s13348-020-00286-2.
APA
Debrouwere, A., Neyt, L., & Vindas Diaz, J. (2021). The nuclearity of Gelfand-Shilov spaces and kernel theorems. COLLECTANEA MATHEMATICA, 72(1), 203–227. https://doi.org/10.1007/s13348-020-00286-2
Chicago author-date
Debrouwere, Andreas, Lenny Neyt, and Jasson Vindas Diaz. 2021. “The Nuclearity of Gelfand-Shilov Spaces and Kernel Theorems.” COLLECTANEA MATHEMATICA 72 (1): 203–27. https://doi.org/10.1007/s13348-020-00286-2.
Chicago author-date (all authors)
Debrouwere, Andreas, Lenny Neyt, and Jasson Vindas Diaz. 2021. “The Nuclearity of Gelfand-Shilov Spaces and Kernel Theorems.” COLLECTANEA MATHEMATICA 72 (1): 203–227. doi:10.1007/s13348-020-00286-2.
Vancouver
1.
Debrouwere A, Neyt L, Vindas Diaz J. The nuclearity of Gelfand-Shilov spaces and kernel theorems. COLLECTANEA MATHEMATICA. 2021;72(1):203–27.
IEEE
[1]
A. Debrouwere, L. Neyt, and J. Vindas Diaz, “The nuclearity of Gelfand-Shilov spaces and kernel theorems,” COLLECTANEA MATHEMATICA, vol. 72, no. 1, pp. 203–227, 2021.
@article{8676939,
  abstract     = {{We study the nuclearity of the Gelfand-Shilov spaces S(M)(W) and S{M}{W}, defined via a weight (multi-)sequence system M and a weight function system W. We obtain characterizations of nuclearity for these function spaces that are counterparts of those for Köthe sequence spaces. As an application, we prove new kernel theorems. Our general framework allows for a unified treatment of the Gelfand-Shilov spaces S(M)(A) and S{M}{A} (defined via weight sequences M and A) and the Beurling-Björck spaces S(ω)(η) and S{ω}{η} (defined via weight functions ω and η). Our results cover anisotropic cases as well.}},
  author       = {{Debrouwere, Andreas and Neyt, Lenny and Vindas Diaz, Jasson}},
  issn         = {{0010-0757}},
  journal      = {{COLLECTANEA MATHEMATICA}},
  keywords     = {{Applied Mathematics,General Mathematics,Gelfand-Shilov spaces,Nuclear spaces,Schwartz kernel theorems,Weight sequence systems,Weight function systems,PSEUDODIFFERENTIAL-OPERATORS}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{203--227}},
  title        = {{The nuclearity of Gelfand-Shilov spaces and kernel theorems}},
  url          = {{http://doi.org/10.1007/s13348-020-00286-2}},
  volume       = {{72}},
  year         = {{2021}},
}

Altmetric
View in Altmetric
Web of Science
Times cited: