Geodesic
Generalized Fourier transform and its applications
Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 581-596.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the generalized Fourier transform treated as an operator on the dual of an arbitrary locally convex space. We give a definition of this operator and establish its basic properties. Special attention is paid to cases in which the range of the generalized Fourier transform coincides with a weighted space of entire functions. The results are applied to finding the orders and types of operators in various spaces. 
@article{MZM_2006_79_4_a9,
     author = {S. V. Panyushkin},
     title = {Generalized {Fourier} transform and its applications},
     journal = {Matemati\v{c}eskie zametki},
     pages = {581--596},
     publisher = {mathdoc},
     volume = {79},
     number = {4},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a9/}
}
TY  - JOUR
AU  - S. V. Panyushkin
TI  - Generalized Fourier transform and its applications
JO  - Matematičeskie zametki
PY  - 2006
SP  - 581
EP  - 596
VL  - 79
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a9/
LA  - ru
ID  - MZM_2006_79_4_a9
ER  - 
%0 Journal Article
%A S. V. Panyushkin
%T Generalized Fourier transform and its applications
%J Matematičeskie zametki
%D 2006
%P 581-596
%V 79
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a9/
%G ru
%F MZM_2006_79_4_a9
S. V. Panyushkin. Generalized Fourier transform and its applications. Matematičeskie zametki, Tome 79 (2006) no. 4, pp. 581-596. http://geodesic.mathdoc.fr/item/MZM_2006_79_4_a9/

[1] Krasichkov I. F., “O zamknutykh idealakh v lokalno vypuklykh algebrakh tselykh funktsii”, Izv. AN SSSR. Ser. matem., 31:1 (1967), 37–60 | Zbl

[2] Krasichkov I. F., “Invariantnye podprostranstva analiticheskikh funktsii. 1: Spektralnyi sintez na vypuklykh oblastyakh”, Matem. sb., 87:4 (1972), 459–489 | Zbl

[3] Napalkov V. V. (ml.), Yulmukhametov R. S., “O preobrazovanii Gilberta v prostranstve Bergmana”, Matem. zametki, 70:1 (2001), 68–78 | MR | Zbl

[4] Musin I. Kh., “O preobrazovanii Fure–Laplasa funktsionalov na vesovom prostranstve beskonechno differentsiruemykh funktsii”, Matem. sb., 191:10 (2000), 57–86 | Zbl

[5] Musin I. Kh., “Teorema Peli–Vinera dlya vesovogo prostranstva beskonechno differentsiruemykh funktsii”, Izv. RAN. Ser. matem., 64:6 (2000), 181–204 | MR | Zbl

[6] Dubinskii Yu. A., Zadacha Koshi v kompleksnoi oblasti, Izd-vo MEI, M., 1996

[7] Gromov V. P., “O polnote znachenii golomorfnoi vektor-funktsii v prostranstve Freshe”, Matem. zametki, 73:6 (2003), 827–840 | MR | Zbl

[8] Mishin S. N., “Poryadok i tip operatora i posledovatelnosti operatorov, deistvuyuschikh v lokalno vypuklykh prostranstvakh”, Uchenye zapiski, no. 3, OGU, Orel, 2002, 47–98

[9] Eliseev I. S., “Perestanovochnost s lineinym differentsialnym operatorom”, Matem. zametki, 26:5 (1979), 719–738 | MR | Zbl

[10] Gelfond A. O., Leontev A. F., “Ob odnom obobschenii ryada Fure”, Matem. sb., 29:3 (1951), 477–500

[11] Leontev A. F., Obobscheniya ryadov eksponent, Nauka, M., 1981 | MR

[12] Pich A., Yadernye lokalno vypuklye prostranstva, Mir, M., 1967 | MR

[13] Robertson A., Robertson V., Funktsionalnyi analiz, Nauka, M., 1979

[14] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz v normirovannykh prostranstvakh, Fizmatgiz, M., 1959 | MR

[15] Taylor B. A., “Some locally convex spaces of entire functions”, Proc. Symp. Pure Math., XI, Amer. Math. Soc., Providence, RI, 1968, 431–467

[16] Gromov V. P., “Analogi razlozheniya Teilora”, Fundament. i prikl. matem., 5:3 (1999), 801–808 | MR | Zbl

[17] Napalkov V. V., “O diskretnykh dostatochnykh mnozhestvakh v nekotorykh prostranstvakh tselykh funktsii”, Dokl. AN SSSR, 250:4 (1980), 809–812 | MR | Zbl

[18] Ehrenpreis L., “Analytically uniform spaces and some applications”, Trans. Amer. Math. Soc., 101:1 (1961), 52–74 | DOI | MR | Zbl