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It is shown that monic orthogonal polynomials on the unit circle are the characteristic polynomials of certain five-diagonal matrices depending on the Schur parameters. This result is achieved… (More)
The CGMV method allows for the general discussion of localization properties for the states of a one-dimensional quantum walk, both in the case of the integers and in the case of the nonnegative… (More)
In this paper, we obtain new results about the orthogonality measure of orthogonal polynomials on the unit circle, through the study of unitary truncations of the corresponding unitary multiplication… (More)
In this paper a general theory of semi-classical matrix orthogonal polynomials is developed. We define the semi-classical linear functionals by means of a distributional equation $D(u A) = u B,$… (More)
Szego's procedure to connect orthogonal polynomials on the unit circle and orthogonal polynomials on [-1,1] is generalized to nonsymmetric measures. It generates the so-called semi-orthogonal… (More)
The radioactive decay equations are solved using an algebraic approach that is simple and easily extensible to branching systems. Two examples are included to show the nature of the approach.
In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove… (More)
In this paper we present some recent results concerning linear spectral transfor- mations of Caratheodory functions. More precisely, given two Caratheodory functions related by a linear spectral… (More)
A time-dependent global fiber-bundle model of fracture with continuous damage is formulated in terms of a set of coupled nonlinear differential equations. A first integral of this set is analytically… (More)