About the Uniform Holder Continuity of Generalized Riemann Function

被引：0
|
作者：
Bastin, F. [1 ]
Nicolay, S. [1 ]
Simons, L. [1 ]
机构：
[1] Univ Liege, Inst Math, B-4000 Liege, Belgium
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2016年 / 13卷 / 01期
关键词：
Holder continuity; continuous wavelet transform; Riemann function; FOURIER-SERIES; NONDIFFERENTIABLE FUNCTION; DIFFERENTIABILITY;
D O I：
10.1007/s00009-014-0501-3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we study the uniform Holder continuity of the generalized Riemann function R-alpha,R-beta (with alpha > 1 and beta > 0) defined by R-alpha,R-beta(x) = Sigma(+infinity)(n=1)sin(pi n(beta)x/n(alpha), x is an element of R, using its continuous wavelet transform. In particular, we show that the exponent we find is optimal. We also analyse the behaviour of R-alpha,R-beta as beta tends to infinity.
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页码：101 / 117
页数：17
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