Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line

Andreas Chatziafratis; Telemachos Hatziafratis

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arXiv · 2403.03718

Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line

Andreas Chatziafratis·Telemachos Hatziafratis

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Abstract

In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, being analytic in the lower half of the complex plane, has natural boundary the axis of the real numbers. We also provide variations and generalizations.

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BibTeX RIS

Andreas Chatziafratis, Telemachos Hatziafratis. 2024-03-06. Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line. https://arxiv.org/abs/2403.03718

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