2014
DOI: 10.1016/j.jat.2014.06.003
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Measurable diagonalization of positive definite matrices

Abstract: In this paper we show that any positive definite matrix V with measurable entries can be written as V = U ΛU * , where the matrix Λ is diagonal, the matrix U is unitary, and the entries of U and Λ 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 polynomia… Show more

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Cited by 2 publications
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“…Remark 2.7. For completeness, we note that the afore mentioned measurable diagonalization is proved in [21] only for families (V (x)) x∈X of positive matrices. However, this easily generalizes to the case considered above.…”
Section: The Birman-schwinger Principle and Hilbert-schmidt Norm Esti...mentioning
confidence: 99%
“…Remark 2.7. For completeness, we note that the afore mentioned measurable diagonalization is proved in [21] only for families (V (x)) x∈X of positive matrices. However, this easily generalizes to the case considered above.…”
Section: The Birman-schwinger Principle and Hilbert-schmidt Norm Esti...mentioning
confidence: 99%