no. 1
On Schwartz's theorem for the motion group
Annales de l'Institut Fourier, Tome 30 (1980) no. 1, pp. 91-107.

Le théorème de Schwartz en synthèse spectrale des fonctions continues sur l’axe réel est généralisé au groupe euclidien du plan. L’analogie unilatérale du théorème de Schwartz pour le groupe euclidien du plan est réduite à l’étude de certains espaces invariants de fonctions continues sur R 2 .

Schwartz’s Theorem in spectral synthesis of continuous functions on the real is generalized to the Euclidean motion group. The rightsided analogue of Schwartz’s Theorem for the motion group is reduced to the study of some invariant subspaces of continuous functions on R 2 .

@article{AIF_1980__30_1_91_0,
     author = {Weit, Yitzhak},
     title = {On {Schwartz's} theorem for the motion group},
     journal = {Annales de l'Institut Fourier},
     pages = {91--107},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {30},
     number = {1},
     year = {1980},
     doi = {10.5802/aif.776},
     mrnumber = {81h:43007},
     zbl = {0407.43008},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.776/}
}
TY  - JOUR
AU  - Weit, Yitzhak
TI  - On Schwartz's theorem for the motion group
JO  - Annales de l'Institut Fourier
PY  - 1980
SP  - 91
EP  - 107
VL  - 30
IS  - 1
PB  - Institut Fourier
PP  - Grenoble
UR  - http://www.numdam.org/articles/10.5802/aif.776/
DO  - 10.5802/aif.776
LA  - en
ID  - AIF_1980__30_1_91_0
ER  - 
%0 Journal Article
%A Weit, Yitzhak
%T On Schwartz's theorem for the motion group
%J Annales de l'Institut Fourier
%D 1980
%P 91-107
%V 30
%N 1
%I Institut Fourier
%C Grenoble
%U http://www.numdam.org/articles/10.5802/aif.776/
%R 10.5802/aif.776
%G en
%F AIF_1980__30_1_91_0
Weit, Yitzhak. On Schwartz's theorem for the motion group. Annales de l'Institut Fourier, Tome 30 (1980) no. 1, pp. 91-107. doi : 10.5802/aif.776. http://www.numdam.org/articles/10.5802/aif.776/

[1] L. Brown, B.M. Schreiber, and B.A. Taylor, Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier, Grenoble, 23 (1973), 125-154. | Numdam | MR | Zbl

[2] L. Ehrenpreis, and F. Mautner, Some properties of the Fourier transform on semi-simple Lie groups II., Trans. Amer. Math. Soc., 84 (1957), 1-55. | MR | Zbl

[3] D.I. Gurevich, Counterexamples to a problem of L. Schwartz, Funct. Anal. Appl., 197 (1975), 116-120. | Zbl

[4] D. Pompeiu, Sur une propriété intégrale des fonctions de deux variables réelles, Bull. Sci. Acad. Royale Belgique (5), 15 (1929), 265-269. | JFM

[5] L. Schwartz, Théorie générale des fonctions moyenne-périodiques, Ann. of Math., 48 (1947), 857-928. | MR | Zbl

[6] Y. Weit, On the one-sided Wiener's theorem for the motion group, to appear in Ann. of Math. | Zbl

[7] L. Zalcman. Analyticity and the Pompeiu problem, Arch. Rational Mech. Anal., 47 (1972), 237-254. | MR | Zbl

Cité par Sources :