2023/01/24 by K. D. Deepak, Jaydeb Sarkar, D., Deepak K. +1 · 2 citations
Mathematics · #15B05 #30D55 #30E05 #32A38 #46J15 #47A13 #47A57 #93C73 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2301.10020
openalex publication_date 2023/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to the contractivity of certain linear functionals. The second one transforms it into nonnegative real numbers via a distance formula. We also solve the Nevanlinna-Pick interpolation problem for bounded analytic functions on the polydisc. Along the way, we solve a perturbation problem for bounded analytic functions. Commutant lifting and interpolation on the polydisc solve two well-known problems in Hilbert function space theory.