Cowling-price theorem and characterization of heat kernel on symmetric spaces

Abstract

Abstract. We extend the uncertainty principle, the Cowling-Price theorem, on noncompact Riemannian symmetric spaces X. We establish a characterization of the heat kernel of the Laplace-Beltrami operator on X from integral estimates of the CowlingPrice type.

A heat kernel version of Cowling-Price theorem for the Laguerre hypergroup

“…A classical version of uncertainty principle, known as Hardy's theorem, was first proved by Hardy [6] on R. Several generalizations of the Hardy's theorem have appeared since, one of these is the Cowling-Price theorem, which was first proved by Cowling and Price in [4]. The following version of Cowling-Price theorem on R n can be found in [2] or [12]. The Cowling-Price theorem has been extended to various settings.…”

Beurling's Theorem and Characterization of Heat Kernel for Riemannian Symmetric Spaces of Noncompact Type

“…Part (a) of Hardy's theorem was proved in [20], [4], [6], while part (b) was proved in [16], [22]. Part (a) of Cowling-Price theorem was proved in [19] and in [17] and part (b) was proved in [18]. Part (a) of Morgan's theorem was proved in [19].…”

“…This shows that Beurling's theorem is the Master theorem. Some of the latter theorems (which follow from Beurling's) were proved independently on symmetric spaces in recent years by many authors (see [20,4,6,16,17,19,22,18] etc.). After completing this work we had the opportunity to see Demange's thesis ( [5]) in which he further generalized theorem 1.2 (see theorem 6.1).…”

A variant of Cowling–Price's and Miyachi's theorems for the Bessel–Struve transform on ℝd

“…The Cowling-Price's principle and their variants have been studied by many authors for various Fourier transforms, for examples (cf. [4][5][6][7]) and others.…”