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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Ranges of joint Laplace-Fourier transforms


Author: Daniel J. Grubb
Journal: Proc. Amer. Math. Soc. 97 (1986), 372-373
MSC: Primary 44A10; Secondary 42A38
DOI: https://doi.org/10.1090/S0002-9939-1986-0835901-6
MathSciNet review: 835901
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Abstract: If $ f \in {L^1}([0,\infty [ \times {\mathbf{R}})$ and $ \hat f(z,s) = \smallint _{ - \infty }^\infty \smallint _0^\infty f(u,v){e^{iuz}}{e^{isv}}dudv$, where $ z \in H = \{ z \in {\mathbf{C}}:\operatorname{Im} \geqslant 0\} ,s \in {\mathbf{R}}$, then $ \hat f(H \times {\mathbf{R}}) \cup \{ 0\} = \hat f({\mathbf{R}} \times {\mathbf{R}}) \cup \{ 0\} $.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0835901-6
Article copyright: © Copyright 1986 American Mathematical Society