Measurable diagonalization of positive definite matrices

JOURNAL OF APPROXIMATION THEORY

卷:185

Article

Quintana, Yamilet¹  Rodriguez, Jose M.² 

[1] Univ Simon Bolivar, Dept Matemat Puras & Aplicadas, Caracas 1080A, Venezuela

[2] Univ Carlos III Madrid, Dept Matemat, Madrid, Spain

关键词: Measurable diagonalization;    Positive definite matrices;    Asymptotic;    Sobolev orthogonal polynomials;    Extremal polynomials;    Weighted Sobolev spaces;   

DOI  :  10.1016/j.jat.2014.06.003

来源: Elsevier

【 摘 要 】

In this paper we show that any positive definite matrix V with measurable entries can be written as V = U Lambda U*, where the matrix Lambda is diagonal, the matrix U is unitary, and the entries of U and Lambda are measurable functions (U* denotes the transpose conjugate of U). This result allows to obtain results about the zero location and asymptotic behavior of extremal polynomials with respect to a generalized non-diagonal Sobolev norm in which products of derivatives of different order appear. The orthogonal polynomials with respect to this Sobolev norm are a particular case of those extremal polynomials. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free