2024/05/23 by Jingbo Xia, Xia, Jingbo, Congquan Yan +5
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2405.14401
openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By now it is a well-known fact that if f is a multiplier for the Drury-Arveson space H2n, and if there is a c>0 such that |f(z)|≥ c for every z∈ B, then the reciprocal function 1/f is also a multiplier for H2n. We show that for such an f and for every t∈ ℝ, ft is also a multiplier for H2n. We do so by deriving a differentiation formula for Rm(fth).Moreover, by this formula the same result holds for spaces Hm,s of the Besov-Dirichlet type. The same technique also gives us the result that for a non-vanishing multiplier f of H2n, log f is a multiplier of H2n if and only if log f is bounded on B.