An extension of deLeeuw’s theorem to the $n$-dimensional rotation group

Dooley, Anthony H.; Gaudry, Garth I.

doi:10.5802/aif.967

An extension of deLeeuw’s theorem to the

n

-dimensional rotation group

Dooley, Anthony H. ; Gaudry, Garth I.

Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 111-135.

Résumé
Abstract

On étudie un processus d’approximation des représentations du groupe $M (n)$ par celles du groupe $S O (n + 1)$ . Comme conséquence on établit une version d’un théorème de DeLeeuw pour les multiplicateurs de Fourier de $L^{p}$ relatif aux “restrictions” d’une fonction sur le dual de $M (n)$ au dual de $S O (n + 1)$ .

We study a method of approximating representations of the group $M (n)$ by those of the group $S O (n + 1)$ . As a consequence we establish a version of a theorem of DeLeeuw for Fourier multipliers of $L^{p}$ that applies to the “restrictions” of a function on the dual of $M (n)$ to the dual of $S O (n + 1)$ .

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.967

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     author = {Dooley, Anthony H. and Gaudry, Garth I.},
     title = {An extension of {deLeeuw{\textquoteright}s} theorem to the $n$-dimensional rotation group},
     journal = {Annales de l'Institut Fourier},
     pages = {111--135},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {34},
     number = {2},
     year = {1984},
     doi = {10.5802/aif.967},
     mrnumber = {86a:43002},
     zbl = {0523.43002},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/aif.967/}
}

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Dooley, Anthony H.; Gaudry, Garth I. An extension of deLeeuw’s theorem to the $n$-dimensional rotation group. Annales de l'Institut Fourier, Tome 34 (1984) no. 2, pp. 111-135. doi : 10.5802/aif.967. https://www.numdam.org/articles/10.5802/aif.967/

Bibliographie
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