A new viewpoint to fourier analysis in fractal space

Abstract

Fractional analysis is an important method for mathematics and engineering, and fractional differentiation inequalities are great mathematical topic for research. In this paper we point out a new viewpoint to Fourier analysis in fractal space based on the local fractional calculus and propose the local fractional Fourier analysis. Based on the generalized Hilbert space, we obtain the generalization of local fractional Fourier series via the local fractional calculus. An example is given to elucidate the signal process and reliable result. © Springer Science+Business Media New York 2013.