Compression on the digital unit sphere.

Allali, Mohamed

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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 $f \times μ_{s} (z) = 0,$ whenever $z \in ℂ^{n}$ and $s > 0$ satisfy the condition that the sphere $S_{s} (z) \subseteq Ann (r, R)$ and ball $B_{r} (0) \subseteq B_{s} (z) .$ 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.

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In this paper we deal with Rarita-Schwinger type operators on spheres and real projective space. First we define the spherical Rarita-Schwinger type operators and construct their fundamental solutions. Then we establish that the projection operators appearing in the spherical Rarita-Schwinger type operators and the spherical Rarita-Schwinger type equations are conformally invariant under the Cayley transformation. Further, we obtain some basic integral formulas related to the spherical...