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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

Yibiao Pan
Yibiao Pan
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pensylvania 15260, U.S.A.
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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

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 36 , Issue 3 , September 1994 , pp. 309 - 311
Copyright
Copyright © Glasgow Mathematical Journal Trust 1994

References

REFERENCES

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