Related papers: A local Paley-Wiener theorem for compact symmetric…

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…

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…

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.

Let G/H be a reductive symmetric space and K a maximal compact subgroup of G. We study Fourier transforms of compactly supported K-finite distributions on G/H and characterize the image of the space of such distributions.

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 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…

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…

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 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 aim of this article is to give an overview of several types of Paley-Wiener theorems occuring in harmonic analysis related to symmetric spaces. This will serve as a motivation for the introduction of the $\Theta$-spherical functions,…

Polynomial invariants are fundamental objects in analysis on Lie groups and symmetric spaces. Invariant differential operators on symmetric spaces are described by Weyl group invariant polynomial. In this article we give a simple criterion…

We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{\alpha, q, a}^{2}$-functions whose q-Weinstein…

Let S(X) be the Schwartz space of compactly supported smooth functions on the p-adic points of a spherical variety X, and let C(X) be the space of Harish-Chandra Schwartz functions. Under assumptions on the spherical variety, which are…

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…

We explore the possibilities of reaching the characterization of eigenfunction of Laplacian as a degenerate case of the inverse Paley-Wiener theorem (characterizing functions whose Fourier transform is supported on a compact annulus) for…

Continuous dually epi-translation invariant valuations on convex functions are characterized in terms of the Fourier-Laplace transform of the associated Goodey-Weil distributions. This description is used to obtain integral representations…

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 (not radial in general) is considered…

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the pointwise decay of their Fourier coefficients [13]. We prove certain analogue…

The $\Theta$-spherical functions generalize the spherical functions on Riemannian symmetric spaces and the spherical functions on non-compactly causal symmetric spaces. In this article we consider the case of even multiplicity functions. We…

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…