RT Journal Article
T1 Measurable diagonalization of positive definite matrices
A1 Quintana, Yamilet
A1 Rodríguez García, José Manuel
AB 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.
PB Elsevier
SN 0021-9045
YR 2014
FD 2014-09-01
LK https://hdl.handle.net/10016/23387
UL https://hdl.handle.net/10016/23387
LA eng
NO The first author was partially supported by a grant from Ministerio de Economía y Competitividad.Dirección General de Investigación Científica y Técnica (MTM2012-36732-03-01),Spain. The second author was partially supported by a grant from CONACYT (CONACYT-UAGI0110/62/10 FON.INST.8/10), México.
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