About the Uniform Holder Continuity of Generalized Riemann Function

作者：Bastin F; Nicolay S; Simons L^*

来源：Mediterranean Journal of Mathematics, 2016, 13(1): 101-117.

DOI：10.1007/s00009-014-0501-3

• Holder continuity
• continuous wavelet transform
• Riemann function

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.

• 出版日期2016-2