Christoffel Functions and Fourier Series for Multivariate Orthogonal Polynomials
نویسندگان
چکیده
منابع مشابه
Christoffel Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials
We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain in particular this is true if they are positive a.e on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex, under far m...
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It follows from Bateman [4] page 213 after setting = 1 2 . It can also be found with slight modi cation in Bateman [5] page122. However we are not aware of any reference where explicit formulas for the Fourier coef cients for Gegenbauer, Jacobi, Laguerre and Hermite polynomials can be found. In this article we use known formulas for the connection coef cients relating an arbitrary orthogonal po...
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We obtain upper bounds for Lebesgue constants (uniform norms) of hyperinterpolation operators via estimates for (the reciprocal of) Christoffel functions, with different measures on the disk and ball, and on the square and cube. As an application, we show that the Lebesgue constant of total-degree polynomial interpolation at the Morrow-Patterson minimal cubature points in the square has an O(de...
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An explicit formula for the Fourier coef cients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials. The methods described here apply in principle to an...
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We establish limits for Christo¤el functions associated with orthogonal rational functions, whose poles remain a xed distance away from the interval of orthogonality [ 1; 1], and admit a suitable asymptotic distribution. The measure of orthogonality is assumed to be regular on [ 1; 1], and to satisfy a local condition such as continuity of 0. As a consequence, we deduce universality limits in ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1995
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1075