Geodesic
On dilation equations and the Hölder continuity of the de Rham functions
Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 309-311

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We use a simple approximation method to prove the Holder continuity of the generalized de Rham functions.1. Consider the following dilatation equationwhere |α|<l/2. Suppose that f is an integrable solution of (1); then f must satisfywhere is the Fourier transform of f, andwhich immediately leads to 
Pan, Yibiao. On dilation equations and the Hölder continuity of the de Rham functions. Glasgow mathematical journal, Tome 36 (1994) no. 3, pp. 309-311. doi: 10.1017/S0017089500030913
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[1] 1.Daubechies, I. and Lagarias, J., Two-scale difference equations I. Existence and global regularity of solutions, SIAM J. Anal. 22 (1991), 1388–1410. Google Scholar | DOI

[2] 2.I. Daubechies and J. Lagarias, Two-scale difference equations II. Local regularity, infinite product of matrices and fractals, to appear. Google Scholar

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