𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A Generalization of Favard′s Theorem for Polynomials Satisfying a Recurrence Relation

✍ Scribed by A.J. Duran

Publisher
Elsevier Science
Year
1993
Tongue
English
Weight
744 KB
Volume
74
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we give the canonical expression for an inner product (defined in (\mathscr{P}), the linear space of real polynomials), for which the set of orthonormal polynomials satisfies a ((2 N+1))-term recurrence relation. This result is a generalization of Favard's theorem about orthogonal polynomials and three-term recurrence relations. Also, we characterize these inner products in terms of symmetric operators. Similar results are proved for some kinds of discrete Sobolev inner products. 1993 Academic Press, Inc

📜 SIMILAR VOLUMES

A short proof for a generalization of Vi
A short proof for a generalization of Vizing's theorem
✍ Claude Berge; Jean Claude Fournier 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB 👁 1 views

## Abstract For a simple graph of maximum degree Δ, it is always possible to color the edges with Δ + 1 colors (Vizing); furthermore, if the set of vertices of maximum degree is independent, Δ colors suffice (Fournier). In this article, we give a short constructive proof of an extension of these re