Paley-Wiener theorems for the Θ-spherical transform: An overview
Several generalizations of the spherical Fourier transform on Riemannian symmetric spaces have emerged in the last decades. All these integral transforms can be viewed as special instances of the Θ-spherical Fourier transform. One of the main questions related to any integral transform is the description of the image of classical function spaces. In this article we discuss several examples of Paley-Wiener type theorems, leading up to and motivating the Paley-Wiener theorem for the Θ-spherical transform.
Publication Source (Journal or Book title)
Acta Applicandae Mathematicae
Ólafsson, G., & Pasquale, A. (2004). Paley-Wiener theorems for the Θ-spherical transform: An overview. Acta Applicandae Mathematicae, 81 (1), 275-309. https://doi.org/10.1023/B:ACAP.0000024203.22722.ec