2021/04/12 by Anindya Kumar Biswas, Biswas, Anindya, Vikramjeet Singh Chandel +1 · 1 citation
Mathematics · #47A56 #Advanced Banach Space Theory #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Primary 47A48 #Secondary 47A57
paper · pdf · doi:10.48550/arxiv.2104.05461
openalex publication_date 2021/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a domain Ω in ℂn and a collection of test functions Ψ on Ω, we consider the complex-valued Ψ-Schur-Agler class associated to the pair (Ω, Ψ). In this article, we characterize interpolating sequences for the associated Banach algebra of which the Ψ-Schur-Agler class is the closed unit ball. When Ω is the unit disc \mathbbD in the complex plane ℂ and the class of test function includes only the identity function on \mathbbD, the aforementioned algebra is the algebra of bounded holomorphic functions on \mathbbD and in this case, our characterization reduces to the well known result by Carleson. Furthermore, we present several other cases of the pair (Ω, Ψ), where our main result could be applied to characterize interpolating sequences which also show the efficacy of our main result.