Asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions

Abstract

We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier hyperfunction, this gives simple notions of asymptotic Fourier and Laplace transforms for vector-valued hyperfunctions, which improves the existing models of Komatsu, Bäumer, Lumer and Neubrander and Langenbruch.

References in corpus (7)

• Weighted vector-valued functions and the $\epsilon$-product
• The approximation property for weighted spaces of differentiable functions
• Desch-Schappacher Perturbation of One-Parameter Semigroups on Locally Convex Spaces
• Vector-valued holomorphic functions in several variables
• The inhomogeneous Cauchy-Riemann equation for weighted smooth vector-valued functions on strips with holes
• Surjectivity of the $\overline{\partial }$-operator between weighted spaces of smooth vector-valued functions
• Asymptotics of Evolution Equations beyond Banach spaces

Cited by in corpus (1)

• The abstract Cauchy problem in locally convex spaces