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MEASURING FUNCTIONS SMOOTHNESS WITH LOCAL FRACTIONAL DERIVATIVES

2001; Springer Science+Business Media; Volume: 4; Issue: 3 Linguagem: Inglês

1311-0454

Kiran M. Kolwankar, Jacques L�vy V�hel,

Approximation Theory and Sequence Spaces

We study a notion of local fractional differentiation, obtained by localizing the classical fractional derivative. We show that it is strongly related with the local Holder exponent, and give an interpretation of this result in terms of 2-microlocal analysis.