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

2016/02/15 by Roman Veprintsev, Veprintsev, Roman
Mathematics · Medicine · #42B35 #42C05 #42C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Medical Imaging Techniques and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1602.04594

openalex publication_date 2016/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a necessary and sufficient condition on a continuous function on\n[-1,1] under which the family of functions on the unit sphere\n mathbbS^d-1 constructed in the described manner is fundamental in\nC( mathbbS^d-1). In our construction of functions and proof of the\nresult, we essentially use Dunkl harmonic analysis.\n

Related

• Dunkl harmonic analysis and fundamental sets of functions on the unit sphere
• An introduction to Dunkl theory and its analytic aspects
• Inscribed squares of level sets of functions on the sphere
• Intertwining operator associated to symmetric groups and summability on the unit sphere
• On sharp Fourier extension from spheres in arbitrary dimensions