# Huygens' principle for the wave equation associated with the trigonometric dunkl-cherednik operators

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4 Citations (Scopus)

## Abstract

Let a be an Euclidean vector space of dimension N, and let k = (k α)α∈ℛ be a multiplicity function related to a root system ℛ. Let Δ(k) be the trigonometric Dunkl-Cherednik differential-difference Laplacian. For (a, t) ∈ exp(a) × ℝ, denote by uk(a,t) the solution to the wave equation Δ(k)uk(a,t) = ∂ttuk(a, t), where the initial data are supported inside a ball of radius R about the origin. We prove that uk has support in the shell {(a, t) ∈ exp(a) × ℝ | |t| - R ≤ ∥ log a∥ ≤ |t| + R} if and only if the root system ℛ is reduced, kα ∈ ℕ for all α ∈ ℛ, and N is odd starting from 3.

Original language English 43-58 16 Mathematical Research Letters 13 1 https://doi.org/10.4310/MRL.2006.v13.n1.a4 Published - Jan 2006 Yes

## Keywords

• Dunkl-Cherednik operators
• Huygens' principle
• Paley-Wiener theorem
• Wave equation

## ASJC Scopus subject areas

• Mathematics(all)

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