Analyse harmonique en dimension infinie : paires de Guelfand généralisées

Abstract : In this Thesis, we first prove a generalisation of Bochner theorem. This result deals with Olshanski spherical pairs which are defined as inductive limits of increasing sequences of Gelfand pairs. By using Choquet's theorem, we establish a Bochner type representation of any element in the set of -biinvariant continuous functions of positive type on Such representation is given via a unique, positive and bounded measure by : Here is the set of spherical functions of positive type on Then we consider the spherical pair where is the infinite dimensional space of square complex matrices with only finite non zero coefficients, and is the infinite dimensional unitary group. By using a result of G. Olshanski and A. Vershik, we determine the set of spherical functions of positive type for the considered spherical pair. This enables us to find a parameterized version of the generalized Bochner theorem which we use to establish an integral representation of continuous functions of negative type in this case
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Marouane Rabaoui. Analyse harmonique en dimension infinie : paires de Guelfand généralisées. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2007. Français. ⟨NNT : 2007METZ028S⟩. ⟨tel-01749014⟩

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