Resumen de The nuclearity of Gelfand–Shilov spaces and kernel theorems

Andreas Debrouwere, Lenny Neyt, Jasson Vindas

• 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.