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Keywords:
spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition
spherical Rarita-Schwinger type operators; Cayley transformation; real projective space; Almansi-Fischer decomposition; Iwasawa decomposition
Summary:
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 Rarita-Schwinger type operators. Second, we define the Rarita-Schwinger type operators on the real projective space and construct their kernels and Cauchy integral formulas.
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