The independence of initial vectors in the subdivision schemes  

作　　者：陈迪荣 李落清 

出　　处：《Science China Mathematics》2002年第11期1439-1445,共7页中国科学：数学（英文版）

基　　金：This work was supported by the National Natural Science Foundation of China(Grant No.10171007).

摘　　要：Starting with an initial vector λ=(λ(k)) k∈? ∈ ?p(?), the subdivision scheme generates a sequence (S a n λ) n=1 ∞ of vectors by the subdivision operator $$S_a \lambda (k) = \sum\limits_{j \in \mathbb{Z}} {\lambda (j)a(k - 2j)} , k \in \mathbb{Z}$$ . Subdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting to understand under what conditions the sequence (S a n λ) n=1 ∞ converges to an Lp-function in an appropriate sense. This problem has been studied extensively. In this paper we show that the subdivision scheme converges for any initial vector in ?p(?) provided that it does for one nonzero vector in that space. Moreover, if the integer translates of the refinable function are stable, the smoothness of the limit function corresponding to the vector A is also independent of λ.Starting with an initial vector λ = (λ(κ))κ∈z ∈ ep(Z), the subdivision scheme generates asequence (Snaλ)∞n=1 of vectors by the subdivision operator Saλ(κ) = ∑λ(j)a(k - 2j), k ∈ Z. j∈zSubdivision schemes play an important role in computer graphics and wavelet analysis. It is very interesting tounderstand under what conditions the sequence (Snaλ)∞n=1 converges to an Lp-function in an appropriate sense.This problem has been studied extensively. In this paper we show that the subdivision scheme converges forany initial vector in ep(Z) provided that it does for one nonzero vector in that space. Moreover, if the integertranslates of the refinable function are stable, the smoothness of the limit function corresponding to the vectorλ is also independent of λ.

关 键 词：SUBDIVISION scheme  joint spectral radius  critical exponent. 

分 类 号：O177[理学—数学]