TY - JOUR
AU - Carlsson, Marcus
AU - Wittsten, Jens
PY - 2017/05/27
Y2 - 2024/04/22
TI - A note on holomorphic functions and the Fourier-Laplace transform
JF - MATHEMATICA SCANDINAVICA
JA - Math. Scand.
VL - 120
IS - 2
SE - Articles
DO - 10.7146/math.scand.a-25612
UR - https://www.mscand.dk/article/view/25612
SP - 225-248
AB - <p><span>We revisit the classical problem of when a given function, which is analytic in the upper half plane $\mathbb{C} _+$, can be written as the Fourier transform of a function or distribution with support on a half axis $(-\infty ,b]$, $b\in \mathbb{R} $. We derive slight improvements of the classical Paley-Wiener-Schwartz Theorem, as well as softer conditions for verifying membership in classical function spaces such asĀ $H^p(\mathbb{C} _+)$.</span></p>
ER -