FRACTAL FUNCTIONS AND WAVELET EXPANSIONS BASED ON SEVERAL SCALING FUNCTIONS
FRACTAL FUNCTIONS AND WAVELET EXPANSIONS BASED ON SEVERAL SCALING FUNCTIONS
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DOI：
10.1006/jath.1994.1085
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发表时间：
1994-09-01
影响因子：
0.9
通讯作者：
MASSOPUST, PR
中科院分区：
文献类型：
--
作者：
GERONIMO, JS;HARDIN, DP;MASSOPUST, PR
给出了利用一类迭代函数系统定义的分形函数构造平移和扩张不变函数空间的一种方法。这些空间推广了在[D]中构造的C-0函数空间。哈丁，b.k essler, p.r. Massopust， J.约。理论71(1992)，104-120]包括，例如，任意光滑函数空间。这些新的函数空间是由几个尺度函数和它们的整数转换生成的。给出了这些函数空间形成L(2)(R)的多分辨率分析的充分必要条件。(C) 1994学术出版社，Inc.
We present a method for constructing translation and dilation invariant functions spaces using fractal functions defined by a certain class of iterated function systems. These spaces generalize the C-0 function spaces constructed in [D. Hardin, B. Kessler, and P. R. Massopust, J. Approx. Theory 71 (1992), 104-120] including, for instance, arbitrarily smooth function spaces. These new function spaces are generated by several scaling functions and their integer-translates. We give necessary and sufficient conditions for these function spaces to form a multiresolution analysis of L(2)(R). (C) 1994 Academic Press, Inc.