Christoffel transformation for a matrix of Bi-variate measures.

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García Ardila, Juan and Mañas Baena, Manuel and Marcellan, Francisco (2019) Christoffel transformation for a matrix of Bi-variate measures. Complex analysis and operator theory, 13 (8). pp. 3979-4005. ISSN 1661-8254

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Official URL: http://dx.doi.org/10.1007/s11785-019-00947-6




Abstract

We consider the sequences of matrix bi-orthogonal polynomials with respect to the bilinear forms <center dot, center dot >((R) over cap) and <center dot, center dot >((L) over cap) < P(z(1)), Q(z(2))((R) over cap) = (TxT)integral P(z(1))dagger L(z(1))d mu(z(1), z(2)) Q(z(2)), P, Q is an element of L-pxp[z] < P(z(1)), Q(z(2))>(L) over cap = (TxT)integral P(z(1))L(z(1))d mu(z(1), z(2))Q(z(2)), where mu(z1, z2) is a matrix of bi-variate measures supported on T x T, with T the unit circle, L pxp[ z] is the set of matrix Laurent polynomials of size p x p and L(z) is a special polynomial in L pxp[ z]. A connection formula between the sequences of matrix Laurent bi-orthogonal polynomials with respect to <center dot, center dot >((R) over cap) and resp <center dot, center dot >((L) over cap) and the sequence of matrix Laurent bi-orthogonal polynomials with respect to d mu(z(1), z(2)) is given.


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© 2019 Springer basel AG.
The authors thank the referees by the careful revision of the manuscript. Their suggestions and remarks have contributed to improve its presentation. The work of Juan C. Garcia-Ardila and Francisco Marcellan has been supported by Direccion General de Investigacion Cientifica y Tecnica, Ministerio de Economia, Industria y Competitividad of Spain, Grant [MTM2015-65888-C4-2-P]. The work of Manuel Manas has been supported by Direccion General de Investigacion Cientifica y Tecnica, Ministerio de Economia, Industria y Competitividad of Spain, Grant [MTM2015-65888-C4-3-P].

Uncontrolled Keywords:Orthogonal laurent polynomials; Unit circle; Perturbations; Extensions.
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:58662
Deposited On:28 Jan 2020 18:52
Last Modified:28 Jan 2020 18:52

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