FRACTAL INTERPOLATION FUNCTIONS ON POST CRITICALLY FINITE SELF-SIMILAR SETS

被引：18
|
作者：
Ruan, Huo-Jun [1 ,2 ]
机构：
[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China
[2] Cornell Univ, Dept Math, Ithaca, NY 14853 USA
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2010年 / 18卷 / 01期
关键词：
Fractal Interpolation Functions; PCF Self-Similar Sets; Energy; Laplacian; CALCULUS;
D O I：
10.1142/S0218348X10004658
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we introduce fractal interpolation functions (FIFs) and linear FIFs on a post critically finite (p.c.f. for short) self-similar set K. We present a sufficient condition such that linear FIFs have finite energy and prove that the solution of Dirichlet problem - Delta(mu)u = f, u vertical bar(partial derivative K) = 0 is a linear FIF on K if f is a linear FIF.
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页码：119 / 125
页数：7
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