Relative asymptotics for orthogonal matrix polynomials with convergent recurrence coefficients
HO Yakhlef, F Marcell�n, MA Pi�ar�- Journal of Approximation Theory, 2001 - Elsevier
HO Yakhlef, F Marcell�n, MA Pi�ar
Journal of Approximation Theory, 2001•ElsevierThe asymptotic behavior of γn (dβ) γn (dα)− 1 and Pn (x, dβ) P− 1n (x, dα) is studied. Here
(γn (.)) n are the leading coefficients of the orthonormal matrix polynomials Pn (x,.) with
respect to the matrix measures dβ and dα which are related by dβ (u)= dα (u)+∑ Nk= 1Mkδ
(u− ck), where Mk are positive definite matrices, δ is the Dirac measure and ck lies outside
the support of dα for k= 1,…, N. Finally, we deduce the asymptotic behavior of Pn (c, dβ) MP*
n (c, dα) when dβ (u)= dα (u)+ Mδ (u− c), with M a positive definite matrix and c outside the�…
(γn (.)) n are the leading coefficients of the orthonormal matrix polynomials Pn (x,.) with
respect to the matrix measures dβ and dα which are related by dβ (u)= dα (u)+∑ Nk= 1Mkδ
(u− ck), where Mk are positive definite matrices, δ is the Dirac measure and ck lies outside
the support of dα for k= 1,…, N. Finally, we deduce the asymptotic behavior of Pn (c, dβ) MP*
n (c, dα) when dβ (u)= dα (u)+ Mδ (u− c), with M a positive definite matrix and c outside the�…
The asymptotic behavior of γn(dβ)γn(dα)−1 and Pn(x,�dβ)P−1n(x,�dα) is studied. Here (γn(.))n are the leading coefficients of the orthonormal matrix polynomials Pn(x,�.) with respect to the matrix measures dβ and dα which are related by dβ(u)=dα(u)+∑Nk=1Mkδ(u−ck), where Mk are positive definite matrices, δ is the Dirac measure and ck lies outside the support of dα for k=1,�…,�N. Finally, we deduce the asymptotic behavior of Pn(c,�dβ)MP*n(c,�dα) when dβ(u)=dα(u)+Mδ(u−c), with M a positive definite matrix and c outside the support of dα.
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