2023/09/12 by Chafiq Benhida, Benhida, Chafiq, Raúl E. Curto +3 · 1 citation
Mathematics · #Holomorphic and Operator Theory #Advanced Differential Equations and Dynamical Systems #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2309.05888
We study a general class of weighted shifts whose weights α are given by αn = √((pn + N)/(pn + D)), where p > 1 and N and D are parameters so that (N,D) ∈ (-1, 1)× (-1, 1). Some few examples of these shifts have appeared previously, usually as examples in connection with some property related to subnormality. In sectors nicely arranged in the unit square in (N,D), we prove that these geometrically regular weighted shifts exhibit a wide variety of properties: moment infinitely divisible, subnormal, k- but not (k+1)-hyponormal, or completely hyperexpansive, and with a variety of well-known functions (such as Bernstein functions) interpolating their weights squared or their moment sequences. They provide subshifts of the Bergman shift with geometric, not linear, spacing in the weights which are moment infinitely divisible. This new family of weighted shifts provides a useful addition to the library of shifts with which to explore new definitions and properties.