ADAPTIVE ORTHONORMAL SYSTEMS FOR MATRIX-VALUED FUNCTIONS

被引：29

作者：

Alpay, Daniel ^{[1
]}

Colombo, Fabrizio ^{[2
]}

Qian, Tao ^{[3
]}

Sabadini, Irene ^{[2
]}

机构：

[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel

[2] Politecn Milan, Dipartimento Matemat, Via E Bonardi,9, I-20133 Milan, Italy

[3] Univ Macau, Dept Math, Ave Univ, Taipa, Macao, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 145卷 / 05期

关键词：

Matrix-valued functions and Hardy spaces; matrix-valued Blaschke products; maximum selection principle; adaptive decomposition; MULTIPLIERS; SPACES; INTERPOLATION;

D O I：

10.1090/proc/13359

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we consider functions in the Hardy space H-2(pxq) defined in the unit disc of matrix-valued functions. We show that it is possible, as in the scalar case, to decompose those functions as linear combinations of suitably modified matrix-valued Blaschke products, in an adaptive way. The procedure is based on a generalization to the matrix-valued case of the maximum selection principle which involves not only selections of suitable points in the unit disc but also suitable orthogonal projections. We show that the maximum selection principle gives rise to a convergent algorithm. Finally, we discuss the case of real-valued signals.

引用

页码：2089 / 2106

页数：18

共 37 条

[1] Some finite-dimensional backward-shift-invariant subspaces in the ball and a related interpolation problem [J].