B-splines, hypergeometric functions, and Dirichlet averages
نویسندگان
چکیده
منابع مشابه
Multivariate complex B-splines and Dirichlet averages
The notion of complex B-spline is extended to a multivariate setting by means of ridge functions employing the known geometric relationship between ordinary B-splines and multivariate B-splines. To derive properties of complex B-splines in R, 1 < s ∈ N, the Dirichlet average has to be generalized to include infinite dimensional simplices △∞. Based on this generalization several identities of mu...
متن کاملMultivariate Complex B-Splines, Dirichlet Averages and Difference Operators
For the Schoenberg B-splines, interesting relations between their functional representation, Dirichlet averages and difference operators are known. We use these relations to extend the B-splines to an arbitrary (infinite) sequence of knots and to higher dimensions. A new Fourier domain representation of the multidimensional complex B-spline is given. 1. Complex B-Splines Complex B-splines are a...
متن کاملMoments of Dirichlet Splines and Their Applications to Hypergeometric Functions
Dirichlet averages of multivariate functions are employed for a derivation of basic recurrence formulas for the moments of multivariate Dirichlet splines. An algorithm for computing the moments of multivariate simplex splines is presented. Applications to hypergeometric functions of several variables are discussed. Introduction. In [9], H.B. Curry and I.J. Schoenberg have pointed out that univa...
متن کاملDouble Dirichelet Averages and Complex B-Splines
A relation between double Dirichlet averages and multivariate complex B-splines is presented. Based on this reationship, a formula for the computation of certain moments of multivariate complex B-splines is derived.
متن کاملMeans of a Dirichlet Process and Multiple Hypergeometric Functions
The Lauricella theory of multiple hypergeometric functions is used to shed some light on certain distributional properties of the mean of a Dirichlet process. This approach leads to several results, which are illustrated here. Among these are a new and more direct procedure for determining the exact form of the distribution of the mean, a correspondence between the distribution of the mean and ...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1991
ISSN: 0021-9045
DOI: 10.1016/0021-9045(91)90006-v