Abstract

Local fractional Fourier series is a generalized Fourier series in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the present chapter is devoted to the theory and applications of local fractional Fourier analysis in generalized Hilbert space. We recall the local fractional Fourier series, the Fourier transform, the generalized Fourier transform, the discrete Fourier transform and fast Fourier transform in fractal space.KeywordsLocal fractional Fourier seriesLocal fractional calculusLocal fractional Fourier transformThe generalized local fractional Fourier transformDiscrete local fractional Fourier transformFast local fractional Fourier transformFractal space

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