On Schwartz's theorem for the motion group

Yitzhak Weit

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 1, page 91-107
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Weit, Yitzhak. "On Schwartz's theorem for the motion group." Annales de l'institut Fourier 30.1 (1980): 91-107. <http://eudml.org/doc/74444>.

@article{Weit1980,
abstract = {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 $\{\bf R\}^2$.},
author = {Weit, Yitzhak},
journal = {Annales de l'institut Fourier},
keywords = {Euclidean Motion Group; Schwartz's Theorem; Spectral Synthesis},
language = {eng},
number = {1},
pages = {91-107},
publisher = {Association des Annales de l'Institut Fourier},
title = {On Schwartz's theorem for the motion group},
url = {http://eudml.org/doc/74444},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Weit, Yitzhak
TI - On Schwartz's theorem for the motion group
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 1
SP - 91
EP - 107
AB - 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 ${\bf R}^2$.
LA - eng
KW - Euclidean Motion Group; Schwartz's Theorem; Spectral Synthesis
UR - http://eudml.org/doc/74444
ER -

References

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  1. [1] L. BROWN, B.M. SCHREIBER, and B.A. TAYLOR, Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier, Grenoble, 23 (1973), 125-154. Zbl0265.46044MR50 #4979
  2. [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. Zbl0079.13201MR18,745f
  3. [3] D.I. GUREVICH, Counterexamples to a problem of L. Schwartz, Funct. Anal. Appl., 197 (1975), 116-120. Zbl0326.46020
  4. [4] D. POMPEIU, Sur une propriété intégrale des fonctions de deux variables réelles, Bull. Sci. Acad. Royale Belgique (5), 15 (1929), 265-269. Zbl55.0139.01JFM55.0139.01
  5. [5] L. SCHWARTZ, Théorie générale des fonctions moyenne-périodiques, Ann. of Math., 48 (1947), 857-928. Zbl0030.15004MR9,428c
  6. [6] Y. WEIT, On the one-sided Wiener's theorem for the motion group, to appear in Ann. of Math. Zbl0604.43002
  7. [7] L. ZALCMAN. Analyticity and the Pompeiu problem, Arch. Rational Mech. Anal., 47 (1972), 237-254. Zbl0251.30047MR50 #582

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