Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4607090 | Journal of Approximation Theory | 2014 | 7 Pages |
Abstract
In this paper we show that any positive definite matrix VV with measurable entries can be written as V=UΛU∗V=UΛU∗, where the matrix ΛΛ is diagonal, the matrix UU is unitary, and the entries of UU and ΛΛ are measurable functions (U∗U∗ denotes the transpose conjugate of UU).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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yamilet Quintana, José M. Rodríguez,