2021/05/03 by Alexandru Aleman, Aleman, Alexandru, Michael Hartz +5
Mathematics · #32A35 #46A13 #47B35 #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.2105.01110
openalex publication_date 2021/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize the common range of the adjoints of cyclic multiplication operators on the Drury--Arveson space. We show that a function belongs to this common range if and only if its Taylor coefficients satisfy a simple decay condition. To achieve this, we introduce the uniform Smirnov class on the ball and determine its dual space. We show that the dual space of the uniform Smirnov class equals the dual space of the strictly smaller Smirnov class of the Drury-Arveson space, and that this in turn equals the common range of the adjoints of cyclic multiplication operators.