MID and safe quotients for GRWS

2023/12/11 by Chafiq Benhida, Benhida, Chafiq, Raúl E. Curto +3
Mathematics · #47 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2312.06390

openalex publication_date 2023/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Geometrically regular weighted shifts (in short, GRWS) are those with weights α(N,D) given by α_n (N,D) = √((pⁿ + N)/(pⁿ + D)), where p > 1 and (N,D) is fixed in the open unit square (-1, 1)× (-1, 1). We study here the zone of pairs (M,P) for which the weight (α(N,D) )/( α(M,P) ) gives rise to a moment infinitely divisible ( \mathcal MID) or a subnormal weighted shift, and deduce immediately the analogous results for product weights α(N,D) α(M,P), instead of quotients. Useful tools introduced for this study are a pair of partial orders on the GRWS.

Citations

• Geometrically regular weighted shifts

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