A family of Sobolev orthogonal polynomials on the unit ball
نویسنده
چکیده
A family of orthonormal polynomials on the unit ball B of R with respect to the inner product
منابع مشابه
Sobolev orthogonal polynomials defined via gradient on the unit ball
An explicit family of polynomials on the unit ball B of R is constructed, so that it is an orthonormal family with respect to the inner product 〈f, g〉 = ρ Z Bd ∇f(x) · ∇g(x)dx + L(fg), where ρ > 0, ∇ is the gradient, and L(fg) is either the inner product on the sphere S or f(0)g(0).
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The purpose of this work is to analyse a family of mutually orthogonal polynomials on the unit ball with respect to an inner product which includes an additional term on the sphere. First, we will get connection formulas relating classical multivariate orthogonal polynomials on the ball with our family of orthogonal polynomials. Then, using the representation of these polynomials in terms of sp...
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For a class of weight functions invariant under reflection groups on the unit ball, a family of orthogonal polynomials is defined via a Rodrigues type formula using the Dunkl operators. Their properties and their relation with several other bases are explored.
متن کاملClifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into ...
متن کاملSome Remarks on a Paper by L. Carlitz
We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain Sobolev orthogonal polynomials.
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 138 شماره
صفحات -
تاریخ انتشار 2006