Affiliation:
1. National Sun Yat-Sen University
2. Commonwealth of Australia
Abstract
Jia and coworkers [1] have shown that with =M_N and ̃=M_1as a pair of locally supported refinable functions, one can construct a function, _N(N being an odd integer) given by _N≔∑_(j=0)^N▒〖((-1)^j)/2 [M_(N+1) (j)+M_N (j+1) ] M_N (2∙-j)〗. Here M_N is a binary spline function of degree N. For r =0, 1, 2, …, N-1, the set {2^(j/2) _N^((r) ) (2^j∙-j);j,k ϵ Z} is a Riesz basis for L_2 (R). This base involves the first N-1 derivatives of the generating function and therefore is useful for dynamical systems with derivative constraints.
Publisher
Trans Tech Publications, Ltd.
Reference11 articles.
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