Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

Yakhlef, Hossain O.; Marcellán, Francisco

doi:10.1007/bf02845271

Anal. Theory Appl.

2002

DOI: 10.1007/bf02845271

|View full text |Cite

Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

Hossain O. Yakhlef

Francisco Marcellán

Abstract: Givetl a positive definite matrix measure (J supported on the unit circle T. then main purpose of this paper is to study the asymptotic behavior of L.(ll)L.({J)-1 and 4).(z;ll)4).(z,{J)-1 where.n(z) = (J(z)

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2007

2021

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 6 publications

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations

Dette

Wagener

2010

Linear Algebra and its Applications

View full text Add to dashboard Cite

We study the moment space corresponding to matrix measures on the unit circle. Moment points are characterized by non-negative definiteness of block Toeplitz matrices. This characterization is used to derive an explicit representation of orthogonal polynomials with respect to matrix measures on the unit circle and to present a geometric definition of canonical moments. It is demonstrated that these geometrically defined quantities coincide with the Verblunsky coefficients, which appear in the Szegö recursions for the matrix orthogonal polynomials. Finally, we provide an alternative proof of the Geronimus relations which is based on a simple relation between canonical moments of matrix measures on the interval [-1,1] and the Verblunsky coefficients corresponding to matrix measures on the unit circle.

show abstract

Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations

Dette

Wagener

2010

Linear Algebra and its Applications

View full text Add to dashboard Cite

show abstract

CMV block matrices for symmetric matrix measures on the unit circle

Fuentes

Garza

2020

Linear Algebra and its Applications

View full text Add to dashboard Cite

Relative asymptotics for orthogonal matrix polynomials with unbounded recurrence coefficients

Yakhlef¹

2007

Integral Transforms and Special Functions

Self Cite

View full text Add to dashboard Cite

The asymptotic behavior of # n (d;) # n (d:) &1 and P n (x, d;) P &1 n (x, d:) is studied. Here (# n (.)) n are the leading coefficients of the orthonormal matrix polynomials P n (x, .) with respect to the matrix measures d; and d: which are related by d;(u)= d:(u)+ N k=1 M k $(u&c k ), where M k are positive definite matrices, $ is the Dirac measure and c k lies outside the support of d: for k=1, ..., N. Finally, we deduce the asymptotic behavior of P n (c, d;) MP n *(c, d:) when d;(u)=d:(u)+M$(u&c), with M a positive definite matrix and c outside the support of d:.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Relative asymptotics for orthogonal matrix polynomials with respect to a perturbed matrix measure on the unit circle

Abstract: Givetl a positive definite matrix measure (J supported on the unit circle T. then main purpose of this paper is to study the asymptotic behavior of L.(ll)L.({J)-1 and 4).(z;ll)4).(z,{J)-1 where.n(z) = (J(z)

Cited by 6 publications

References 10 publications

Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations

Matrix measures on the unit circle, moment spaces, orthogonal polynomials and the Geronimus relations

CMV block matrices for symmetric matrix measures on the unit circle

Relative asymptotics for orthogonal matrix polynomials with unbounded recurrence coefficients

Contact Info

Product

Resources

About