2017/06/12 by Daniel Girela, Noel Merchán · 1 citation
Mathematics · #Advanced Banach Space Theory #Algebraic and Geometric Analysis #Analytic function #Borel measure #Generalization #Hankel matrix #Hardy space #Hilbert space #Holomorphic and Operator Theory #Invariant (physics) #Matrix (chemical analysis) #Matrix function #Operator (biology) #math.CV #msc:30H10 #msc:47B35
paper · pdf · doi:10.1007/s00020-017-2409-3
published as Integral Equations and Operator Theory 89 (2017), 581-594 · arXiv admin note: text overlap with arXiv:1612.08304
arxiv created 2017/06/12 · openalex created_date 2017/06/23 · openalex publication_date 2017/11/02 · arxiv updated 2017/12/01 · openalex updated_date 2026/08/05
If μ is a positive Borel measure on the interval [0, 1) we let \mathcal Hμ be the Hankel matrix \mathcal Hμ=(μn, k)n,k≥ 0 with entries μn, k=μn+k, where, for n = 0, 1, 2, … , μn denotes the moment of order n of μ. This matrix induces formally the operator Hμ(f)(z)= ∑n=0∞(∑k=0∞ μn,kak)zn on the space of all analytic functions f(z)=∑k=0^∞ akzk, in the unit disc \mathbb D . This is a natural generalization of the classical Hilbert operator. In this paper we improve the results obtained in some recent papers concerning the action of the operators Hμ on Hardy spaces and on Möbius invariant spaces.