The Christoffel functions \(A_{n}(d \mu)\) associated with a general nonnegative measure \(\mu\) on \(\mathbb{R}^{d}\) are studied. The asymptotics of \(A_{n}(d \mu)\) are derived for \(\mu\) supported on \([-1,1]^{d}\). The estimates of \(A_{n}(d \mu)\) are used to study the summability of the mult
Christoffel type functions for m-orthogonal polynomials
โ Scribed by Ying Guang Shi
- Book ID
- 108158988
- Publisher
- Elsevier Science
- Year
- 2005
- Tongue
- English
- Weight
- 298 KB
- Volume
- 137
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let \(W_{x}(x):=\exp \left(-|x|^{x}\right), x \in \mathbb{R}, x>0\). For \(\alpha \leqslant 1\), we obtain upper and lower bounds for the Christoffel functions for the weight \(W_{x}^{2}\) over the whole MhaskarRahmanov-Saff interval, and deduce inequalities for spacing of zeros of orthogonal polyno
The Christoffel functions for orthogonal polynomials are extended to the case of L m extremal polynomials with an even integer m and their properties are given.
For the special type of weight functions on circular arc we study the asymptotic behavior of the Christoffel kernel off the arc and of the Christoffel function inside the arc. We prove Totik's conjecture for the Christoffel function corresponding to such weight functions.