Best Approximation in Hardy Spaces and by Polynomials, with Norm Constraints

被引：0
作者：
Juliette Leblond
Jonathan R. Partington
Elodie Pozzi
机构：
[1] INRIA,School of Mathematics
[2] Team APICS,undefined
[3] University of Leeds,undefined
[4] INRIA,undefined
[5] Team ATHENA,undefined
来源：
Integral Equations and Operator Theory | 2013年 / 75卷
关键词：
Primary 30H10; 41A50; 47B35; Secondary 65J22; Hardy space; extremal problem; polynomial approximation; rational approximation; truncated Toeplitz operator;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Two related approximation problems are formulated and solved in Hardy spaces of the disc and annulus. With practical applications in mind, truncated versions of these problems are analysed, where the solutions are chosen to lie in finite-dimensional spaces of polynomials or rational functions, and are expressed in terms of truncated Toeplitz operators. The results are illustrated by numerical examples. The work has applications in systems identification and in inverse problems for PDEs.
引用
收藏
页码：491 / 516
页数：25
相关论文
共 52 条
[1]  
Abrahamse M.B.(1971)Toeplitz operators in multiply connected regions Bul. Math. Soc. 77 449-454
[2]  
Alpay D.(1995)Traces of Hardy functions and reproducing kernel Hilbert spaces Archiv. der Math. 64 490-499
[3]  
Leblond J.(2004)On the existence of eigenvalues of Toeplitz operators on planar regions Proc. Amer. Math. Soc. 132 3007-3018
[4]  
Aryana C.P.(2010)Bounded extremal and Cauchy-Laplace problems on the sphere and shell J.Fourier Anal. Appl. 16 177-203
[5]  
Clancey K.F.(2003)Asymptotic estimates for interpolation and constrained approximation in Int. Eq. Oper. Theory 45 269-299
[6]  
Atfeh B.(1998) by diagonalization of Toeplitz operators Constr. Approx. 14 41-56
[7]  
Baratchart L.(1996)Hardy approximation to Constr. Approx. 12 423-435
[8]  
Leblond J.(1997) functions on subsets of the circle with 1 ≤ I.E.E.E. Trans. Automat. Cont. 42 1318-1325
[9]  
Partington J.R.(1999) < ∞ Studia. Math. 136 255-269
[10]  
Baratchart L.(2003)Hardy approximation to J. Math. Anal. Appl. 280 176-187
123456