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Analyse harmonique sur les cônes satellites

Abstract : The main idea of this work is the study of the analysis and the geometry of some prehomogenous spaces and ordered symmetric spaces, via their realization in the euclidian Jordan algebras. In first, we work on the singularities of the zêta integrals of some prehomogenous spaces. The method involved is the production of Bernstein-Sato identities for the relative invariants. Then, we realize geometrically some ordered symmetric spaces, called the satellite cones, in terms of euclidian Jordan algebras. Finally, we study the analysis of satellite cones, via a program and a conjecture made by G. Olafsson and A. Pasquale. Using the theory of radial parts, we construct a family of Bernstein-Sato polynomials, which allows the study of the spherical functions of the satllite cones. They are used to rectify the conjecture, and prove it in the context of satellite cones.
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https://hal.univ-lorraine.fr/tel-01746590
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Submitted on : Thursday, March 29, 2018 - 10:40:51 AM
Last modification on : Saturday, October 16, 2021 - 11:18:03 AM

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  • HAL Id : tel-01746590, version 1

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Yann Angeli. Analyse harmonique sur les cônes satellites. Autre [cond-mat.other]. Université Henri Poincaré - Nancy 1, 2001. Français. ⟨NNT : 2001NAN10195⟩. ⟨tel-01746590⟩

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