CLASSIFICATION OF REFINABLE SPLINES IN Rd
نویسندگان
چکیده
A refinable spline in R is a compactly supported refinable function whose support can be decomposed into simplices such that the function is a polynomial on each simplex. The best known refinable splines in R are the box splines. Refinable splines play a key role in many applications, such as numerical computation, approximation theory and computer aided geometric design. Such functions have been classified in one dimension in [6, 14]. In higher dimensions Sun [17] characterized those splines when the dilation matrices are of the form A = mI where m ∈ Z and I is the identity matrix. For more general dilation matrices the problem becomes more complex. In this paper we give a complete classification of refinable splines in R for arbitrary dilation matrices A ∈ Md(Z).
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