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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.

Item Type: | Article |
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Additional Information: | © 2019 Springer basel AG. |

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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