✦ LIBER ✦

Properties of Multivariate Homogeneous Orthogonal Polynomials

✍ Scribed by Brahim Benouahmane; Annie Cuyt

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 165 KB
Volume: 113
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.2000.3565

No coin nor oath required. For personal study only.

✦ Synopsis

It is well-known that the denominators of Pade approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pade -type approximants from so-called generating polynomials and then improving the order of approximation by imposing orthogonality conditions on the generating polynomials.

In the multivariate case, a similar construction is possible when dealing with the multivariate homogeneous Pade approximants introduced by the second author. Moreover it is shown here, that several well-known properties of the zeroes of classical univariate orthogonal polynomials, in the case of a definite linear functional, generalize to the multivariate homogeneous case. For the multivariate homogeneous orthogonal polynomials, the absence of common zeroes is translated to the absence of common factors.

📜 SIMILAR VOLUMES

Orthogonal Homogeneous Polynomials

✍ A. Fryant; A. Naftalevich; M.K. Vemuri 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 71 KB

An addition formula, Pythagorean identity, and generating function are obtained for orthogonal homogeneous polynomials of several real variables. Application is made to the study of series of such polynomials. Results include an analog of the Funk-Hecke theorem.

Semiclassical Multiple Orthogonal Polyno

Semiclassical Multiple Orthogonal Polynomials and the Properties of Jacobi–Bessel Polynomials

✍ A.I. Aptekarev; F. Marcellán; I.A. Rocha 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 429 KB

This paper deals with Hermite Pade polynomials in the case where the multiple orthogonality condition is related to semiclassical functionals. The polynomials, introduced in such a way, are a generalization of classical orthogonal polynomials (Jacobi, Laguerre, Hermite, and Bessel polynomials). They

Some Properties of the Homogeneous Multi

Some Properties of the Homogeneous Multivariate Pareto (IV) Distribution

✍ H.C. Yeh 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 215 KB

On Lacunary Sums of Orthogonal Polynomia

On Lacunary Sums of Orthogonal Polynomials

✍ A. Kroo 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 345 KB

Uniform Subexponential Growth of Orthogo

Uniform Subexponential Growth of Orthogonal Polynomials

✍ R. Szwarc 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 211 KB

We show that if orthonormal polynomials \(p_{n}\) have asymptotically periodic recurrence coefficients, then they have uniform subexponential growth on the support of orthogonalizing measure. This is an alternative proof of results of P. Nevai, V. Totik, and J. Zhang (J. Approx. Theory 67, 1991, 215

On the Roots of Orthogonal Polynomials a

On the Roots of Orthogonal Polynomials and Euler-Frobenius Polynomials

✍ F. Dubeau; J. Savoie 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 433 KB