Symbol calculus on the affine group "ax + b"
The symbol calculus on the upper half plane is studied from the viewpoint of the Kirillov theory of orbits. The main result is the -estimates for Fuchs type pseudodifferential operators.
Tempered reductive homogeneous spaces
Let be a semisimple algebraic Lie group and a reductive subgroup. We find geometrically the best even integer for which the representation of in is almost . As an application, we give a criterion which detects whether this representation is tempered.
Terme constant des fonctions tempérées sur un espace symétrique réductif.
The Abel transform and shift operators
The Capelli identity and unitary representations
The evolution and Poisson kernels on nilpotent meta-abelian groups
Let S be a semidirect product S = N⋊ A where N is a connected and simply connected, non-abelian, nilpotent meta-abelian Lie group and A is isomorphic to , k>1. We consider a class of second order left-invariant differential operators on S of the form , where , and for each is left-invariant second order differential operator on N and , where Δ is the usual Laplacian on . Using some probabilistic techniques (e.g., skew-product formulas for diffusions on S and N respectively) we obtain an...
The Fatou theorem for NA groups - a negative result
The Fourier transform of functions satisfying the Lipschitz condition on rank 1 symmetric spaces.
The Fourier Transform of Harish-Chandra's c-Function and Inversion of the Able Transform.
The Helgason-Fourier transform for symmetric spaces. II.
The infinite Brownian loop on a symmetric space.
The irreducible unitary -spherical representations of
The Lévy-Khintchine-Formula for Dissipative Distributions.
The Logarithmic Hardy-Littlewood-Sobolev Inequlity and Extremals of Zeta Functions on Sn.
The non-semi-simple term in the trace formula for rank one lattices.
The Plancherel formula for the pseudo-riemannian space
The Poisson Transform for Split Reductive Symmetric Spaces.
The principal series for a reductive symmetric space. I. -fixed distribution vectors
The reciprocal of the beta function and Whittaker functions
In this paper we derive, using the Gauss summation theorem for hypergeometric series, a simple integral expression for the reciprocal of Euler’s beta function. This expression is similar in form to several well-known integrals for the beta function itself.We then apply our new formula to the study of Whittaker functions, which are special functions that arise in the Fourier theory for automorphic forms on the general linear group. Specifically, we deduce explicit integral representations of “fundamental”...
The 𝔳-radial Paley-Wiener theorem for the Helgason Fourier transform on Damek-Ricci spaces
We prove the Paley-Wiener theorem for the Helgason Fourier transform of smooth compactly supported 𝔳-radial functions on a Damek-Ricci space S = NA.