Quadratic decomposition of symmetric semi-classical polynomial sequences of even class: an example from the case<i>s</i> = 2

Maroni, P.; Tounsi, M. Ihsen

doi:10.1080/10236198.2011.579118

Cited by 20 publications

(4 citation statements)

References 9 publications

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“…Several aspects of the quadratic decomposition of univariate orthogonal polynomials have been already considered in the literature, see for instance, [2,4,7,11,12,[14][15][16][17][18][19] and the references therein. In [15,16] the quadratic decomposition (1.1) has been generalized for polynomial sequences non necessarily symmetric, [13] by using arbitrary polynomials of degree 2 and 1 replacing x 2 and x, respectively, in (1.1), with special attention to the quadratic transformation x 2 − 1 relating Gegenbauer and Jacobi polynomials ( [10]), or even by means of a simple cubic decomposition, as we can read for instance in [5].…”

Section: Motivationmentioning

confidence: 99%

Quadratic Decomposition of Bivariate Orthogonal Polynomials

2023

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We describe the relation between the systems of bivariate orthogonal polynomial associated to a symmetric weight function and associated to some particular Christoffel modifications of the quadratic decomposition of the original weight. We analyze the construction of a symmetric bivariate orthogonal polynomial sequence from a given one, orthogonal to a weight function defined on the first quadrant of the plane. In this description, a sort of Bäcklund type matrix transformations for the involved three term matrix coefficients plays an important role. Finally, we take as a case study relations between the classical orthogonal polynomials defined on the ball and those on the simplex.

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Section: Motivationmentioning

confidence: 99%

Quadratic Decomposition of Bivariate Orthogonal Polynomials

2023

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“…[14, p.34]), and several further studies have showed the potencial of the quadratic decomposition in the study of symmetric and non-symmetric orthogonal polynomial sequences (e.g. [10,18]).…”

Section: Introductionmentioning

confidence: 99%

On a 2-Orthogonal Polynomial Sequence via Quadratic Decomposition

Mesquita

2020

Math.Comput.Sci.

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We apply a symbolic approach of the general quadratic decomposition of polynomial sequences -presented in a previous article referenced herein -to polynomial sequences fulfilling specific orthogonal conditions towards two given functionals u 0 , u 1 belonging to the dual of the vector space of polynomials with coefficients in C. The general quadratic decomposition produces four new sets of polynomials whose properties are investigated with the help of the mentioned symbolic approach together with further commands which inquire relevant features, as for instance, the classical character of a polynomial sequence. The computational results are detailed for a wide range of choices of parameters and co-recursive type polynomial sequences are also explored.

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“…If we are dealing with an orthogonal sequence the first fundamental property to consider is the regularity [16,17,21,24]. We can also study the same problem for specific properties like semi-classical [5,29], Laguerre-Hahn [3,4] or Appell characters [14], among others. Also, the decomposition can reveal interesting connections between a sequence and its components and allows a deep study of all families involved as it was the case in [15,32].…”

Section: Introductionmentioning

confidence: 99%