Related papers: A Paley-Wiener theorem for distributions on reduct…

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized.

In our previous articles "A local Paley-Wiener theorem for compact symmetric spaces", Adv. Math. 218 (2008), 202--215, and "Fourier series on compact symmetric spaces" (submitted) we studied Fourier series on a compact symmetric space…

We study the Fourier transform for compactly supported distributional sections of complex homogeneous vector bundles on symmetric spaces of non-compact type $X = G/K$. We prove a characterisation of their range. In fact, from Delorme's…

We show that Arthur's Paley-Wiener theorem for K-finite compactly supported smooth functions on a real reductive Lie group G of the Harish-Chandra class can be deduced from the Paley-Wiener theorem we established in the more general setting…

The Fourier coefficients of a smooth $K$-invariant function on a compact symmetric space $M=U/K$ are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we…

The Fourier coefficients F(t) of a function f on a compact symmetric space U/K are given by integration of f against matrix coefficients of irreducible representations of U. The coefficients depend on a spectral parameter t, which…

Paley-Wiener type theorems describe the image of a given space of functions, often compactly supported functions, under an integral transform, usually a Fourier transform on a group or homogeneous space. Several authors have studied…

We prove a Paley-Wiener Theorem for a class of symmetric spaces of the compact type, in which all root multiplicities are even. This theorem characterizes functions of small support in terms of holomorphic extendability and exponential type…

We formulate and prove a version of Paley-Wiener theorem for the inverse Fourier transform on non-compact Riemannian symmetric spaces and Heisenberg groups. The main ingredient in the proof is the Gutzmer's formula.

Let $F$ be a nonarchimedean local field, and $G$ the group of $F$-points of a c onnected quasisplit reductive group defined on $F$; in this paper, we will study the distributions on $G$ which are invariant by conjugation, and the vector spa…

The images of Hermite and Laguerre Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterised. These are used to characterise the Schwartz class of rapidly decreasing functions. The image of the space…

We define the Fourier transform of compactly supported Whittaker functions on a reductive p-adic group and we characterize the image of this transformation.

Let ${\boldsymbol{G}}$ be a connected reductive group defined over a non--Archimedean local field $F$. Put $G={\boldsymbol{G}}(F)$. Let $\theta$ be an $F$--automorphism of ${\boldsymbol{G}}$, and let $\omega$ be a smooth character of $G$.…

We extend the Paley--Wiener theorem for riemannian symmetric spaces to an important class of infinite dimensional symmetric spaces. For this we define a notion of propagation of symmetric spaces and examine the direct (injective) limit…

We develop real Paley-Wiener theorems for classes ${\mathcal S}_\omega$ of ultradifferentiable functions and related $L^{p}$-spaces in the spirit of Bang and Andersen for the Schwartz class. We introduce results of this type for the…

One of the important questions related to any integral transform on a manifold M or on a homogeneous space G/K is the description of the image of a given space of functions. If M=G/K, where (G,K) is a Gelfand pair, then the harmonic…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with the help of a family of weight functions is considered in this paper. For…

Let $G$ be (the rational points of) a connected reductive group over a local non-archimedean field $F$. In this article we formulate and prove a property of an $F$-spherical homogeneous $G$-space (which in addition satisfies the finite…

This paper conducts a geometric analysis of the Joint-Eigenspace Fourier transform of the symmetric space of the non-compact type. Our study shows how the Poisson transform builds up the well-known Helgason Fourier transform for an analysis…

A space of entire functions of several complex variables rapidly decreasing on ${\mathbb R}^n$ and such that their growth along $i{\mathbb R}^n$ is majorized with a help of a family of weight functions is considered in the paper. For this…