A multidimensional Tauberian theorem for Laplace transforms of ultradistributions

Abstract

We obtain a multidimensional Tauberian theorem for Laplace transforms of Gelfand-Shilov ultradistributions. The result is derived from a Laplace transform characterization of bounded sets in spaces of ultradistributions with supports in a convex acute cone of R n , also established here.2010 Mathematics Subject Classification. 40E05, 44A10, 46F12.

On the space of ultradistributions vanishing at infinity

“…The latter is achieved in this article by exploiting the mapping properties of the short-time Fourier transform (STFT) on the spaces 9 B 1ω and DL 1 ω . The STFT has recently proved to be a powerful tool to study the structural and linear topological properties of (generalized) function spaces; see [6,7,14,16,17].…”