
The nuclearity of Gelfand-Shilov spaces and kernel theorems
- Author
- Andreas Debrouwere (UGent) , Lenny Neyt (UGent) and Jasson Vindas Diaz (UGent)
- 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
- |
- |
- 335.28 KB
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8676939
- 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: