Uniformity in the Fourier inversion formula with applications to Laplace transforms

2025/03/29 by Alexopoulos, Joannis
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2503.23210

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 C₀-semigroups.

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