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This paper deals with the analysis of the orthogonality of a monic polynomial sequencedefined as a linear combination of a sequence of monic orthogonal polynomialswithwherefor. Moreover, we obtain the relation between the corresponding linear functionals as well as an explicit expression for the sequence of monic orthogonal polynomials. We obtain the connection between the Jacobi matrices associated withand, respectively, by using an LU factorization. Some special cases of the above type relation are analysed. [ABSTRACT FROM AUTHOR]

In this paper, we show that two Zariski dense subgroups consisting of hyperbolic elements in SO(n+1,n)⋉R2n+1 with the same marked Margulis invariant, are conjugate. We also consider in affine deformations an analogue of quasifuchsian deformation of Fuchsian groups. [Copyright &y& Elsevier]

Abstract: In a previous paper, the author introduced a new class of multivariate rational interpolants, which are called Optimal Padé-type Approximants (OPTA). There, for this class of rational interpolants, which extends classical univariate Padé Approximants, a direct extension of the “de Montessus de Ballore''s Theorem” for meromorphic functions in several variables is established. In the univariate case, this theorem ensures uniform convergence of a row of Pade Approximants when the denominator degree equals the number of poles (counting multiplicities) in a certain disc. When one overshoots the number of poles when fixing the denominator degree, convergence in measure or capacity has been proved and, under certain additional restrictions, the uniform convergence of a subsequence of the row. The author tackles the latter case and studies its generalization to functions in several variables by using OPTA. [Copyright &y& Elsevier]