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.

On étudie un processus d’approximation des représentations du groupe M(n) par celles du groupe SO(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 SO(n+1).

We study a method of approximating representations of the group M(n) by those of the group SO(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 SO(n+1).

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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},
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     number = {2},
     year = {1984},
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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. http://archive.numdam.org/articles/10.5802/aif.967/

[1] J.-L. Clerc, Sommes de Riesz et multiplicateurs sur un groupe de Lie compact, Ann. Inst. Fourier, Grenoble, 24, 1 (1974), 149-172. | Numdam | MR | Zbl

[2] A. H. Dooley and J. W. Rice, Contractions of rotation groups and their representations. To appear, Math. Proc. Camb. Phil. Soc. | Zbl

[3] E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vol. I, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963.

[4] E. Hewitt and K. A. Ross, Abstract harmonic analysis, Vol. II, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1970.

[5] J. E. Humphreys, Introduction to Lie algebras and representation theory, Graduate Texts in Mathematics, Vol. 9. Springer-Verlag, New York-Berlin, 1972. | MR | Zbl

[6] A. Kleppner and R. L. Lipsman, The Plancherel formula for group extensions, Ann. Sci. Ecole Norm. Sup., 5 (1972), 459-516. | Numdam | MR | Zbl

[7] K. De Leeuw, On Lp multipliers, Ann. of Math., (2), 81 (1965), 364-379. | MR | Zbl

[8] R. L. Rubin, Harmonic analysis on the group of rigid motions of the Euclidean plane, Studia Math., LXII (1978), 125-141. | MR | Zbl

[9] J. P. Serre, Algèbres de Lie semi-simples complexes, W. A. Benjamin, Inc., New York, 1966. | MR | Zbl

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