Uniformity in the Fourier inversion formula with applications to Laplace transforms
Functional Analysis
2025-04-01 v1
Abstract
We systematically find conditions which yield locally uniform convergence in the Fourier inversion formula in one and higher dimensions. We apply the gained knowledge to the complex inversion formula of the Laplace transform to extend known results for Banach space-valued functions and, specifically, for C_0-semigroups.
Keywords
Cite
@article{arxiv.2503.23210,
title = {Uniformity in the Fourier inversion formula with applications to Laplace transforms},
author = {Joannis Alexopoulos},
journal= {arXiv preprint arXiv:2503.23210},
year = {2025}
}
Comments
15 pages; no figures