000150976 001__ 150976
000150976 005__ 20251017144610.0
000150976 0247_ $$2doi$$a10.1016/j.jat.2021.105579
000150976 0248_ $$2sideral$$a123961
000150976 037__ $$aART-2021-123961
000150976 041__ $$aeng
000150976 100__ $$0(orcid)0000-0003-3636-276X$$aCantero, M.J.$$uUniversidad de Zaragoza
000150976 245__ $$aA CMV connection between orthogonal polynomials on the unit circle and the real line
000150976 260__ $$c2021
000150976 5060_ $$aAccess copy available to the general public$$fUnrestricted
000150976 5203_ $$aM. Derevyagin, L. Vinet and A. Zhedanov introduced in Derevyagin et al. (2012) a new connection between orthogonal polynomials on the unit circle and the real line. It maps any real CMV matrix into a Jacobi one depending on a real parameter ¿. In Derevyagin et al. (2012) the authors prove that this map yields a natural link between the Jacobi polynomials on the unit circle and the little and big -1 Jacobi polynomials on the real line. They also provide explicit expressions for the measure and orthogonal polynomials associated with the Jacobi matrix in terms of those related to the CMV matrix, but only for the value ¿=1 which simplifies the connection –basic DVZ connection–. However, similar explicit expressions for an arbitrary value of ¿ –(general) DVZ connection– are missing in Derevyagin et al. (2012). This is the main problem overcome in this paper. This work introduces a new approach to the DVZ connection which formulates it as a two-dimensional eigenproblem by using known properties of CMV matrices. This allows us to go further than Derevyagin et al. (2012), providing explicit relations between the measures and orthogonal polynomials for the general DVZ connection. It turns out that this connection maps a measure on the unit circle into a rational perturbation of an even measure supported on two symmetric intervals of the real line, which reduce to a single interval for the basic DVZ connection, while the perturbation becomes a degree one polynomial. Some instances of the DVZ connection are shown to give new one-parameter families of orthogonal polynomials on the real line.
000150976 536__ $$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E26-17R$$9info:eu-repo/grantAgreement/ES/DGA-FEDER/E48-20R$$9info:eu-repo/grantAgreement/ES/MICINN-AEI-FEDER/MTM2017-89941-P
000150976 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttps://creativecommons.org/licenses/by/4.0/deed.es
000150976 590__ $$a0.993$$b2021
000150976 591__ $$aMATHEMATICS$$b155 / 333 = 0.465$$c2021$$dQ2$$eT2
000150976 592__ $$a0.689$$b2021
000150976 593__ $$aAnalysis$$c2021$$dQ2
000150976 593__ $$aNumerical Analysis$$c2021$$dQ2
000150976 593__ $$aApplied Mathematics$$c2021$$dQ2
000150976 594__ $$a1.8$$b2021
000150976 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000150976 700__ $$aMarcellán, F.
000150976 700__ $$0(orcid)0000-0001-9248-293X$$aMoral, L.$$uUniversidad de Zaragoza
000150976 700__ $$0(orcid)0000-0002-3050-9540$$aVelázquez, L.$$uUniversidad de Zaragoza
000150976 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000150976 773__ $$g266 (2021), 105579 [22 pp.]$$pJ. approx. theory$$tJournal of Approximation Theory$$x0021-9045
000150976 8564_ $$s457048$$uhttps://zaguan.unizar.es/record/150976/files/texto_completo.pdf$$yVersión publicada
000150976 8564_ $$s1657180$$uhttps://zaguan.unizar.es/record/150976/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000150976 909CO $$ooai:zaguan.unizar.es:150976$$particulos$$pdriver
000150976 951__ $$a2025-10-17-14:16:59
000150976 980__ $$aARTICLE