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Relative asymptotics for orthogonal matrix polynomials
Branquinho, A.; Marcellán, F.; Mendes, A.In this paper we study sequences of matrix polynomials that satisfy a non-symmetric recurrence relation. To study this kind of sequences we use a vector interpretation of the matrix orthogonality. In the context of these sequences of matrix polynomials we introduce the concept of the generalized matrix Nevai class and we give the ratio asymptotics between two consecutive polynomials belonging to this class. We ...
Vector interpretation of the matrix orthogonality on the real line
Branquinho, A.; Marcellán, F.; Mendes, A.In this paper we study sequences of vector orthogonal polynomials. The vector orthogonality presented here provides a reinterpretation of what is known in the literature as matrix orthogonality. These systems of orthogonal polynomials satisfy three-term recurrence relations with matrix coefficients that do not obey to any type of symmetry. In this sense the vectorial reinterpretation allows us to study a non-sy...
Coherent pairs of linear functionals on the unit circle
Branquinho, A.; Moreno, A. Foulquié; Marcellán, F.; Rebocho, M. N.In this paper we extend the concept of coherent pairs of measures from the real line to Jordan arcs and curves. We present a characterization of pairs of coherent measures on the unit circle: it is established that if ([mu]0,[mu]1) is a coherent pair of measures on the unit circle, then [mu]0 is a semi-classical measure. Moreover, we obtain that the linear functional associated with [mu]1 is a specific rational...
Hardy-type theorem for orthogonal functions with respect to their zeros. The Ja...
Abreu, L. D.; Marcellan, F.; Yakubovich, S. B.Motivated by the G.H. Hardy's 1939 results [G.H. Hardy, Notes on special systems of orthogonal functions II: On functions orthogonal with respect to their own zeros, J. London Math. Soc. 14 (1939) 37-44] on functions orthogonal with respect to their real zeros [lambda]n, , we will consider, under the same general conditions imposed by Hardy, functions satisfying an orthogonality with respect to their zeros with...
WKB Approximation and Krall-Type Orthogonal Polynomials
Álvarez-Nodarse, R.; Marcellán, F.; Petronilho, J.We give a unified approach to the Krall-type polynomials orthogonal withrespect to a positive measure consisting of an absolutely continuous one‘perturbed’ by the addition of one or more Dirac deltafunctions. Some examples studied by different authors are considered from aunique point of view. Also some properties of the Krall-type polynomials arestudied. The three-term recurrence relation is calculated explici...
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