2025/02/02 by Ramlal Debnath, Debnath, Ramlal, Deepak Kumar Pradhan +3
Computer Science · #30H05 #30J05 #32A35 #46J15 #47A15 #47A56 #Advanced Algebra and Logic #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.2502.00727
openalex publication_date 2025/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Characteristic functions of linear operators are analytic functions that serve as complete unitary invariants. Such functions, as long as they are built in a natural and canonical manner, provide representations of inner functions on a suitable domain and make significant contributions to the development of various theories in Hilbert function spaces. In this paper, we solve this problem in polydiscs. In particular, we present a concrete description of the characteristic functions of tuples of commuting pure contractions and, consequently, provide a description of inner functions on polydiscs.