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On dilation equations and the Hölder continuity of the de Rham functions
Published online by Cambridge University Press: 18 May 2009
Abstract
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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 equation
where |α|<l/2. Suppose that f is an integrable solution of (1); then f must satisfy
where 
is the Fourier transform of f, and
which immediately leads to
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- Copyright © Glasgow Mathematical Journal Trust 1994
References
REFERENCES
1.Daubechies, I. and Lagarias, J., Two-scale difference equations I. Existence and global regularity of solutions, SIAM J. Anal. 22 (1991), 1388–1410.CrossRefGoogle Scholar
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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