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Quelques problèmes d'analyse harmonique sur certains groupes de Lie exponentiels

Abstract : This thesis studies some problems in Harmonic Analysis on exponential Lie groups. In the first chapter, we recall the basic notions concerning these particular Lie groups as well as their representations theory. In the second chapter, we study the Lp-Fourier transform for a special class of exponential Lie groups, the strong -regular exponential Lie groups. Moreover, we provide an estimate of its norm using the orbit method. In the third chapter, we generalize the classical Fourier inversion theorem to the class of connected, simply connected, nilpotent Lie groups. This is done via variable Lie structures. The last part presents some applications of this inversion theorem. We obtain a new decomposition of the L (G) space, where G denotes a connected, simply connected nilpotent Lie group. We write L (G) as the closure of a sum of left invariant subspaces which coincide with the sets of weak solutions, in L (G), of certain systems of differential equations
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Laurent Scuto. Quelques problèmes d'analyse harmonique sur certains groupes de Lie exponentiels. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 2005. Français. ⟨NNT : 2005METZ008S⟩. ⟨tel-01752424⟩

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