Geodesic
Laplace transformation of Fourier hyperfunctions and related classes of analytic functionals
Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 3, pp. 291-309

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The spaces of analytic functionals of two types are introduced: spaces of the type $\Phi'$ characterized by Fourier transformation and including the space of Fourier hyperfunctions as a particular case, and spaces of the type $\Lambda'$ characterized by the Laplace transformation. The Laplace transformation on the spaces of the type $\Lambda'$ and connection between spaces of the type $\Phi'$ and $\Lambda'$ are studied. In particular, conditions for the Fourier hyperfunction to possess Laplace transformation are found. 
@article{TMF_1977_33_3_a0,
     author = {V. V. Zharinov},
     title = {Laplace transformation of {Fourier} hyperfunctions and related classes of analytic functionals},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {291--309},
     publisher = {mathdoc},
     volume = {33},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_33_3_a0/}
}
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V. V. Zharinov. Laplace transformation of Fourier hyperfunctions and related classes of analytic functionals. Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 3, pp. 291-309. http://geodesic.mathdoc.fr/item/TMF_1977_33_3_a0/