Mean periodic functions on phase space and the Pompeiu problem with a twist
Annales de l'Institut Fourier, Volume 45 (1995) no. 4, p. 1007-1035

We show that when f is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by f contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.

Si f est une fonction moyenne périodique, tempérée, sur le groupe d’Heisenberg réduit, alors le sous-espace fermé engendré par f, invariant par translation et rotation, contient une fonction sphérique élémentaire. À l’aide d’un théorème de Paley-Wiener pour la transformation de Fourier-Weyl, nous formulons une conjecture pour les fonctions moyenne périodiques quelconques.

@article{AIF_1995__45_4_1007_0,
     author = {Thangavelu, Sundaram},
     title = {Mean periodic functions on phase space and the Pompeiu problem with a twist},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {45},
     number = {4},
     year = {1995},
     pages = {1007-1035},
     doi = {10.5802/aif.1482},
     zbl = {0831.43003},
     mrnumber = {96m:43009},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1995__45_4_1007_0}
}
Thangavelu, Sundaram. Mean periodic functions on phase space and the Pompeiu problem with a twist. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 1007-1035. doi : 10.5802/aif.1482. http://www.numdam.org/item/AIF_1995__45_4_1007_0/

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