A projective description of generalized Gelfand-Shilov spaces of Roumieu type

Abstract

We provide a projective description for a class of generalized Gelfand-Shilov spaces of Roumieu type. In particular, our results apply to the classical Gelfand-Shilov spaces and weighted $L^{\infty }$-spaces of ultradifferentiable functions of Roumieu type.

10 pages

References in corpus (4)

• On quasianalytic classes of Gelfand-Shilov type. Parametrix and convolution
• On weighted inductive limits of spaces of ultradifferentiable functions and their duals
• Optimal embeddings of ultradistributions into differential algebras
• Solution to the first Cousin problem for vector-valued quasianalytic functions

Cited by in corpus (2)

• Fourier characterizations and non-triviality of Gelfand-Shilov spaces, with applications to Toeplitz operators
• A multidimensional Tauberian theorem for Laplace transforms of ultradistributions