Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607740 | Journal of Approximation Theory | 2010 | 10 Pages |
Abstract
For r>0 let AP(Dr) denote the set of 2Ï-periodic functions which are analytic on the closed rectangle Dr={zâC:0â¤Re zâ¤2Ï,|Im z|â¤r}, and let AP[0,2Ï]=AP(D0). For a positive integer n let Zn={tn,1,tn,2,â¦,tn,n} be a set of nodes in the interval [0,2Ï) such that tn,10 such that the sequence (TnZf) converges to f uniformly on [0,2Ï] for every fâAP(Dr) and every sequence of nodal sets Zn which satisfy equation (â). The main results are summarized as ln(4hâ1)â¤r(h)â¤min{2ln(h+1+h2),ln(4h2+16h4â1)}.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Hua Liu, Jinyuan Du, Guozhu Shang,