Smoothness of rank M scaling functions

Elsevier

2009-03-23T01:47:04Z

2009-03-23T01:47:04Z

2002

This article investigates the smoothness of rank M scaling functions and gives some numerical results. Smoothness of a scaling function φ is studied by introducing an exponent s_p(φ), which is represented by the spectral radius of the transfer operator associated with the reduced symbol of φ. A direct method for estimating the spectral radius is also proposed and used to obtain quite sharp estimates for s_p(φ) and for the Hölder exponents. In fact, numerical experiments on s_1(φ) for a certain class of scaling functions give estimates for their Hölder exponents much better than those obtained by the Sobolev estimates, which are known so far, combined with the Sobolev imbedding theorem.

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Applied and Computational Harmonic Analysis, 13 (2002), pp.116 -137

http://hdl.handle.net/10212/1876

en

https://doi.org/10.1016/S1063-5203(02)00502-X

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Journal Article

Article