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.

引用

页码：119 / 125

页数：7

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