Twisted spherical means in annular regions in ℂ n and support theorems
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, p. 2509-2523
Let Z( Ann (r,R)) be the class of all continuous functions f on the annulus Ann (r,R) in ℂ n with twisted spherical mean f×μ s (z)=0, whenever z∈ℂ n and s>0 satisfy the condition that the sphere S s (z)⊆ Ann (r,R) and ball B r (0)⊆B s (z). In this paper, we give a characterization for functions in Z( Ann (r,R)) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in ℂ n which improve some of the earlier results.
Soit Z( Ann (r,R)) la classe de toutes les fonctions continues sur l’anneau Ann (r,R) de ℂ n de moyenne sphérique tordue f×μ s (z)=0, pour tout z∈ℂ n et s>0 tels que la sphère S s (z)⊆ Ann (r,R) et la boule B r (0)⊆B s (z). Dans cet article, nous donnons une caractérisation des fonctions dans Z( Ann (r,R)) en termes de leur coefficients dans le développement en harmoniques sphériques. Nous prouvons également des théorèmes de support pour les moyennes sphériques tordues dans ℂ n qui améliorent certains résultats antérieurs.
DOI : https://doi.org/10.5802/aif.2498
Classification:  43A85,  44A35,  53C65
Keywords: Heisenberg group, twisted spherical means, twisted convolution, spherical harmonics, support theorems 
@article{AIF_2009__59_6_2509_0,
     author = {Rawat, Rama and Srivastava, R.K.},
     title = {Twisted spherical means in annular regions in $\mathbb{C}^n$ and support theorems},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     pages = {2509-2523},
     doi = {10.5802/aif.2498},
     zbl = {pre05673904},
     mrnumber = {2640928},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2009__59_6_2509_0}
}

Rawat, Rama; Srivastava, R.K. Twisted spherical means in annular regions in $\mathbb{C}^n$ and support theorems. Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2509-2523. doi : 10.5802/aif.2498. https://aif.centre-mersenne.org/item/AIF_2009__59_6_2509_0/

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