Taylor coefficients of inner functions and Beurling's theorem for the shift

2013/10/30 by Dragan Vukotić, Vukotić, Dragan
Mathematics · #30B10 #30H10 #30J05 #46E20 #47A15 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Spectral Theory in Mathematical Physics #math.CV #msc:30B10 #msc:30H10 #msc:30J05 #msc:46E20 #msc:47A15

paper · pdf · doi:10.48550/arxiv.1310.8271

openalex publication_date 2013/10/30 · arxiv created 2014/12/30 · arxiv updated 2014/12/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The purpose of this expository note is to give a proof of a Schur-type theorem that characterizes the inner functions in terms of their Taylor coefficients. In view of Beurling's theorem, this provides a sequential characterization of the shift-invariant subspaces of ℓ².

Related

• A Generalization of Beurling's Theorem and Quasi-Inner Functions
• An Abstract Beurling's Theorem for Several Complex Variables I
• A canonical decomposition of strong L²-functions
• Inner functions in reproducing kernel spaces
• A Beurling Theorem for almost-invariant subspaces of the shift operator