A spherical Wiener-Plancherel formula

Uperieure S Ormale N Ecole Département De Mathématiques Et Applications a Plancherel Formula on Sp 4 a Plancherel Formula on Sp 4 a Plancherel Formula on Sp 4

In HC], Harish-Chandra derived the Plancherel formula on p-adic groups. However, to have an explicit formula, one will have to compute the measures appearing in the formula. Here, we compute Plancherel measures on Sp 4 over p-adic elds explicitly.

The plancherel formula for sl(2) over a local field.

More than two decades ago, in his classical paper on the irreducible unitary representations of the Lorentz group, V. Bargmann initiated the concrete study of Fourier analysis on real Lie groups and obtained the analogue of the classical Fourier expansion theorem in the case of the Lorentz group. Since then the general theory for real semisimple Lie groups has been extensively developed, chiefl...

Plancherel Formula for the 2 x 2 Real Unimodular Group.

The Plancherel decomposition for a reductive symmetric space I. Spherical functions

We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the most continuous part of the Plancherel formula by means of a residue calculus. In the course of the present paper we also obtain new proofs of the uniform t...

Plancherel and Paley-wiener Theorems for an Index Integral Transform Vu Kim Tuan, Ali Ismail

where Jν(x) is the Bessel function of the first kind of order ν [1], and =z denotes the imaginary part of z. An extensive table of integral transforms involving the Bessel functions in the kernels is collected in [6]. Since the integration in (2) is with respect to the order of the Bessel function, such a pair of integral transforms is called index transform. Details about many other index tran...