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arXiv · 2503.23210

Uniformity in the Fourier inversion formula with applications to Laplace transforms

Joannis Alexopoulos
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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.

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Joannis Alexopoulos. 2025-03-29. Uniformity in the Fourier inversion formula with applications to Laplace transforms. https://arxiv.org/abs/2503.23210

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