相关论文: Elementary proofs of Paley-Wiener theorems for the…

In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on Rd. More precisely, we characterize the functions in the Schwartz space S(IRd) and in L2k(Rd) whose Dunkl transform has bounded, unbounded, convex and…

We examine the Sobolev space associated with the linear canonical Dunkl transform and explore some properties of the linear canonical Dunkl operators. Building on these results, we establish a real Paley-Wiener theorem for the linear…

In this paper we present generalisations of Paley-Wiener type theorems to Mellin and (Laplace-)Fourier transforms of rapidly decreasing smooth functions with positive support and log-polyhomogeneous asymptotic expansion at zero. This…

We argue that a proof of the geometrical form of the Paley-Wiener theorems for the Dunkl transform in the literature is not correct.

We conjecture a geometrical form of the Paley-Wiener theorem for the Dunkl transform and prove three instances thereof, one of which involves a limit transition from Opdam's results for the graded Hecke algebra. Furthermore, the connection…

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,…

In this article, we establish first a geometric Paley-Wiener theorem for the Dunkl transform in the crystallographic case. Next we obtain an optimal bound for the $L^p\to L^p$ norm of Dunkl translations in dimension 1. Finally we describe…

We systematically develop real Paley-Wiener theory for the Fourier transform on R^d for Schwartz functions, L^p-functions and distributions, in an elementary treatment based on the inversion theorem. As an application, we show how versions…

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…

In this paper we establish a version of the Paley-Wiener theorem of Fourier analysis in the frame of the Mellin transform. We provide two different proofs, one involving complex analysis arguments, namely the Riemann surface of the…

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…

In this paper we present another proofs of the geometrical forms of Paley-Wiener theorems for the Dunkl transform given in [15], and we prove inversion formulas for the Dunl interwining operator Vk and for its dual tVk and we deduce the…

We argue that another proof by Trimeche of the geometrical form of the Paley-Wiener theorems for the Dunkl transform is not correct.

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…

We prove two theorems of Paley and Wiener in the slice regular setting. As an application, we can compute the reproducing kernel for the slice regular Paley-Wiener space, and obtain a related sampling theorem.

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 define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional $K$-functional in $L^p$-space with the Dunkl weight. As application, we prove direct and inverse theorems of approximation theory, and some…

Consider the (Helgason-) Fourier transform on a Riemannian symmetric space G/K. We give a simple proof of the L^p-Schwartz space isomorphism theorem (0 <p \le 2) for K-finite functions. The proof is a generalization of J.-Ph. Anker's proof…

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…

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…