A Fourier--Laplace Transform (Open)

Summary: Find a function $f$ from the Schwartz space $S(\mathbb R)$ of rapidly decreasing smooth functions with support in $\overline{\mathbb R^{+}} := \{x \in \mathbb R: \; x \ge 0\}$ whose Fourier transform has no zeros in $\overline{\mathbb C^{+}} := \{z: \; \im z \ge 0\}$.

Classification: Primary, Classical Analysis; Secondary, Other

A. E. Merzon
Institute of Physics and Mathematics
University of Michoacan of San Nicolas de Hidalgo
Ciudad Universitaria, 58090
Morelia, Michoacan, Mexico
Email: anatoli@ifm.umich.mx
Phone: +52 443-340-45-30
Fax: +52 443-322-35-00 ext 4133

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