Geodesic
Laplace transformation of Fourier hyperfunctions and related classes of analytic functionals
Teoretičeskaâ i matematičeskaâ fizika, Tome 33 (1977) no. 3, pp. 291-309 
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/
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     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},
     year = {1977},
     volume = {33},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1977_33_3_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, «Nauka», 1976 | MR | Zbl

[2] M. Sato, J. Fac. Sci. Univ. Tokyo, 8 (1969), 139 ; 8 (1960), 387 | MR | Zbl

[3] M. Sato, T. Kawai, M. Kashiwara, Lecture Notes in Math., 287 (1973), 264 | MR

[4] T. Kawai, J. Fac. Sci. Univ. Tokyo, sec. 1A, 17 (1970), 467 | MR | Zbl

[5] A. Kaneko, J. Fac. Sci. Univ. Tokyo, sec. 1A, 19 (1972), 321 | MR | Zbl

[6] A. Kaneko, Proc. Japan. Acad., 48 (1972), 651 | DOI | MR | Zbl

[7] S. Nagamachi, N. Mugibayashi, Commun. Math. Phys., 46 (1976), 119 | DOI | MR | Zbl

[8] S. Nagamachi, N. Mugibayashi, Commun. Math. Phys., 49 (1976), 257 | DOI | MR | Zbl

[9] R. Rokafellar, Vypuklyi analiz, «Mir», 1973

[10] H. Komatsu, J. Math. Soc. Japan, 19 (1967), 366 | DOI | MR | Zbl

[11] I. M. Gelfand, G. E. Shilov, Obobschennye funktsii, vyp. 2, Fizmatgiz, 1958 | MR

[12] A. G. Kostyuchenko, B. S. Mityagin, Tr. Mosk. matem. ob-va, 9 (1960), 283 | MR | Zbl

[13] B. S. Mityagin, Tr. Mosk. matem. ob-va, 9 (1960), 317 | MR | Zbl

[14] V. P. Palamodov, Lineinye differentsialnye operatory s postoyannymi koeffitsientami, «Nauka», 1967 | MR

[15] M. A. Solovev, TMF, 15 (1973), 3 | MR | Zbl

[16] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, «Nauka», 1964 | MR

[17] M. Sato, Lecture Notes in Physics, 39 (1975), 13 | DOI | Zbl

[18] A. G. Zemanyan, Integralnye preobrazovaniya obobschennykh funktsii, «Nauka», 1974 | MR

[19] L. Schwartz, Medd. Lunds Univ. mat. Semin., Supplementband, 1952, 196 | MR | Zbl

[20] K. McKennon, J. für Mathematik, 281 (1974), 164 | MR