223 research outputs found
Coherent pairs of measures and Markov-Bernstein inequalities
All the coherent pairs of measures associated to linear functionals and
, introduced by Iserles et al in 1991, have been given by Meijer in 1997.
There exist seven kinds of coherent pairs. All these cases are explored in
order to give three term recurrence relations satisfied by polynomials. The
smallest zero of each of them of degree has a link with the
Markov-Bernstein constant appearing in the following Markov-Bernstein
inequalities: where . The seven kinds of
three term recurrence relations are given. In the case where and , explicit upper and lower bounds are given
for , and the asymptotic behavior of the corresponding
Markov-Bernstein constant is stated. Except in a part of one case, is proved in all the cases.Comment: 32 page
On the non-normal Padé table in a non-commutative algebra
AbstractIn the non-commutative algebra the blocks in the table of orthogonal polynomials and therefore in the Padé table are not square, and generally it is impossible to say anything on the structure of these blocks except for infinite blocks. This last case is extensively studied here for the non-normal Padé table, the non-normal table P of orthogonal polynomials, and the non-normal ϵ-table. Some examples of illustration of different situations are given
Inégalités de Landau-Kolmogorov dans des espaces de Sobolev
Ce travail est dédié à l étude des inégalités de type Landau-Kolmogorov en normes L2. Les mesures utilisées sont celles d Hermite, de Laguerre-Sonin et de Jacobi. Ces inégalités sont obtenues en utilisant une méthode variationnelle. Elles font intervenir la norme d un polynômes p et celles de ces dérivées. Dans un premier temps, on s'intéresse aux inégalités en une variable réelle qui font intervenir un nombre quelconque de normes. Les constantes correspondantes sont prises dans le domaine où une certaine forme bilinéaire est définie positive. Ensuite, on généralise ces résultats aux polynômes à plusieurs variables réelles en utilisant le produit tensoriel dans L2 et en faisant intervenir au plus les dérivées partielles secondes. Pour les mesures d'Hermite et de Laguerre-Sonin, ces inégalités sont étendues à toutes les fonctions d'un espace de Sobolev. Pour la mesure de Jacobi on donne des inégalités uniquement pour les polynômes d'un degré fixé par rapport à chaque variable.This thesis is devoted to Landau-Kolmogorov type inequalities in L2 norm. The measures which are used, are the Hermite, the Laguerre-Sonin and the Jacobi ones. These inequalities are obtained by using a variational method and the involved the square norms of a polynomial p and some of its derivatives. Initially, we focused on inequalities in one real variable that involve any number of norms. The corresponding constants are taken in the domain where a certain biblinear form is positive definite. Then we generalize these results to polynomials in several real variables using the tensor product in L2 and involving at most the second partial derivatives. For the Hermite and Laguerrre-Sonin cases, these inequalities are extended to all functions of a Sobolev space. For the Jacobi case inequalities are given only for polynomials of degree fixed with respect to each variable.ROUEN-INSA Madrillet (765752301) / SudocSudocFranceF
Impact of the Maturation of Human Primary Bone-Forming Cells on Their Behavior in Acute or Persistent Staphylococcus aureus Infection Models
International audienc
A Rodrigues-type formula for Gegenbauer matrix polynomials
This paper centers on the derivation of a Rodrigues-type formula for the Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is givenThis research has been supported by the Universitat Politecnica de Valencia under grant PAID-06-11-2020.Defez Candel, E. (2013). A Rodrigues-type formula for Gegenbauer matrix polynomials. Applied Mathematics Letters. 26:899-903. https://doi.org/10.1016/j.aml.2013.04.001S8999032
Higher analogues of the discrete-time Toda equation and the quotient-difference algorithm
The discrete-time Toda equation arises as a universal equation for the
relevant Hankel determinants associated with one-variable orthogonal
polynomials through the mechanism of adjacency, which amounts to the inclusion
of shifted weight functions in the orthogonality condition. In this paper we
extend this mechanism to a new class of two-variable orthogonal polynomials
where the variables are related via an elliptic curve. This leads to a `Higher
order Analogue of the Discrete-time Toda' (HADT) equation for the associated
Hankel determinants, together with its Lax pair, which is derived from the
relevant recurrence relations for the orthogonal polynomials. In a similar way
as the quotient-difference (QD) algorithm is related to the discrete-time Toda
equation, a novel quotient-quotient-difference (QQD) scheme is presented for
the HADT equation. We show that for both the HADT equation and the QQD scheme,
there exists well-posed -periodic initial value problems, for almost all
\s\in\Z^2. From the Lax-pairs we furthermore derive invariants for
corresponding reductions to dynamical mappings for some explicit examples.Comment: 38 page
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