Contributions to the Hypergeometric Function Theory of Heckman and Opdam: Sharp Estimates, Schwartz Space, Heat Kernel

By Bruno Schapira. 2006

142 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications (2012, methodology): “[26] B. Schapira: Contributions to the hypergeometric function theory of Heckman and Opdam: sharp estimates, Schwartz space, heat kernel, Geom.”
An Introduction to Dunkl Theory and Its Analytic Aspects (2016, methodology): “8 were obtained in [80] (see also [78]) and [71].”
Opdam's hypergeometric functions: product formula and convolution structure in dimension 1 (2010, unknown): “β) 0 is stricly positive and is bounded above by ( C(1+x)e−ρx if x≥0, Ceρx if x≤0. (ii) For every λ∈Rand x∈R, we have (G α,β) λ (x) ≤ G( 0 (x). Proof. These estimates are proved in full generality in [15] (see Lemma 3.1, Proposition 3.1.a and Theorem 3.2). For the reader’s convenience, we include a ”
Positivity of the Jacobi–Cherednik intertwining operator and its dual (2010, background): “Important results have yet been obtained in this direction [12] but despite to recent interesting results [14], applications remain restricted, in particular for lack of precise information on the eigenfunctions of these operators T .”