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Titlebook: Geometric and Harmonic Analysis on Homogeneous Spaces and Applications; TJC 2019, Djerba, Tu Ali Baklouti,Hideyuki Ishi Conference proceedi

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Nicolas Carnot,Vincent Koen,Bruno TissotWe classify all irreducible coherent state representations of the holomorphic automorphism group of the tube domain over the dual of the Vinberg cone.
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The Compression Semigroup of the Dual Vinberg Cone,We investigate the semigroup associated with the dual Vinberg cone and prove its triple and Ol’shanskiĭ polar decompositions. Moreover, we show that the semigroup does not have the contraction property with respect to the canonical Riemannian metric on the cone.
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,An Extension of Pizzetti’s Formula Associated with the Dunkl Operators,We give an extension of Pizzetti’s formula associated with the Dunkl operators. It gives an explicit formula for the Dunkl inner product of an arbitrary function and a homogeneous Dunkl harmonic polynomial on the unit sphere.
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https://doi.org/10.1057/9781137465337inin algebras of Hom-type. To this end, we provide a general key construction that establish a relationship between identities of some class of Hom-algebras and ordinary algebras. Moreover, we discuss a new concept of Hom-bialgebra, in relation with universal enveloping Hom-algebras. A study based on primitive elements is provided.
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