AFFINE FRACTAL FUNCTIONS AS BASES OF CONTINUOUS FUNCTIONS

被引：9
|
作者：
Navascues, M. A. [1 ]
机构：
[1] Univ Zaragoza, Dept Matemat Aplicada, Escuela Ingn & Arquitectura, Zaragoza 50018, Spain
来源：
QUAESTIONES MATHEMATICAE | 2014年 / 37卷 / 03期
关键词：
28A80; 58C05; 65D05; 65D10; 26A18; Fractal interpolation functions; iterated function systems; Schauder bases;
D O I：
10.2989/16073606.2013.779607
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The objective of the present paper is the study of affine transformations of the plane, which provide self-affine curves as attractors. The properties of these curves depend decisively of the coefficients of the system of affnities involved. The corresponding functions are continuous on a compact interval. If the scale factors are properly chosen one can define Schauder bases of C[a, b] composed by affine fractal functions close to polygonals. They can be chosen bounded. The basis constants and the biorthogonal sequence of coefficient functionals are studied.
引用
收藏
页码：415 / 428
页数：14
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