Dunkl harmonic analysis and fundamental sets of functions on the unit sphere

2016/03/06 by Roman Veprintsev, Veprintsev, Roman
Computer Science · Mathematics · #42B35 #42C05 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1603.01832

openalex publication_date 2016/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using Dunkl theory, we introduce into consideration some weighted L_p-spaces on [-1,1] and on the unit Euclidean sphere \mathbbS^d-1, d≥ 2. Then we define a family of linear bounded operators \V_κ^p(x)\colon x∈\mathbbS^d-1\ acting from the L_p-space on [-1,1] to the L_p-space on \mathbbS^d-1, 1≤ p

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