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Christoffel type functions for m-orthogonal polynomials

โœ 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

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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

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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

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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.