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共查询到20条相似文献,搜索用时 0 毫秒
1.
Jeong Keun Lee L.L. Littlejohn 《Journal of Mathematical Analysis and Applications》2006,322(2):1001-1017
We consider polynomials in two variables which satisfy an admissible second order partial differential equation of the form
(∗) 相似文献
2.
Classical orthogonal polynomials in two variables are defined as the orthogonal polynomials associated to a two-variable moment functional satisfying a matrix analogue of the Pearson differential equation. Furthermore, we characterize classical orthogonal polynomials in two variables as the polynomial solutions of a matrix second order partial differential equation.
AMS subject classification 42C05, 33C50Partially supported by Ministerio de Ciencia y Tecnología (MCYT) of Spain and by the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02, Junta de Andalucía, G.I. FQM 0229 and INTAS Project 2000-272. 相似文献
3.
4.
Yuan Xu 《Integral Transforms and Special Functions》2015,26(2):134-151
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples. 相似文献
5.
Antonio J. Durán 《Journal of Approximation Theory》2011,163(12):1815-1833
We find structural formulas for a family (Pn)n of matrix polynomials of arbitrary size orthogonal with respect to the weight matrix e−t2eAteA∗t, where A is certain nilpotent matrix. It turns out that this family is a paradigmatic example of the many new phenomena that show the big differences between scalar and matrix orthogonality. Surprisingly, the polynomials Pn, n≥0, form a commuting family. This commuting property is a genuine and miraculous matrix setting because, in general, the coefficients of Pn do not commute with those of Pm, n≠m. 相似文献
6.
The aim of this paper is to investigate some general properties of common zeros of orthogonal polynomials in two variables for any given region D⊂R2 from a view point of invariant factor. An important result is shown that if X0 is a common zero of all the orthogonal polynomials of degree k then the intersection of any line passing through X0 and D is not empty. This result can be used to settle the problem of location of common zeros of orthogonal polynomials in two variables. The main result of the paper can be considered as an extension of the univariate case. 相似文献
7.
María Álvarez de Morales Lidia Fernández Teresa E. Pérez Miguel A. Piñar 《Numerical Algorithms》2007,45(1-4):153-166
In this paper, we consider bivariate orthogonal polynomials associated with a quasi-definite moment functional which satisfies
a Pearson-type partial differential equation. For these polynomials differential properties are obtained. In particular, we
deduce some structure and orthogonality relations for the successive partial derivatives of the polynomials.
相似文献
8.
In this paper a systematic study of the orthogonal polynomial solutions of a second order partial difference equation of hypergeometric type of two variables is done. The Pearson's systems for the orthogonality weight of the solutions and also for the difference derivatives of the solutions are presented. The orthogonality property in subspaces is treated in detail, which leads to an analog of the Rodrigues-type formula for orthogonal polynomials of two discrete variables. A classification of the admissible equations as well as some examples related with bivariate Hahn, Kravchuk, Meixner, and Charlier families, and their algebraic and difference properties are explicitly given. 相似文献
9.
Some examples of orthogonal matrix polynomials satisfying odd order differential equations 总被引:1,自引:1,他引:1
It is well known that if a finite order linear differential operator with polynomial coefficients has as eigenfunctions a sequence of orthogonal polynomials with respect to a positive measure (with support in the real line), then its order has to be even. This property no longer holds in the case of orthogonal matrix polynomials. The aim of this paper is to present examples of weight matrices such that the corresponding sequences of matrix orthogonal polynomials are eigenfunctions of certain linear differential operators of odd order. The weight matrices are of the form W(t)=tαe-teAttBtB*eA*t, | where A and B are certain (nilpotent and diagonal, respectively) N×N matrices. These weight matrices are the first examples illustrating this new phenomenon which are not reducible to scalar weights. 相似文献
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