Regularity of fractal interpolation functions via wavelet transform

In the present paper, the regularity of a Fractal Interpolation Function (FIF) is studied using wavelet transform. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation which FIF satisfies. By this method, it is shown that the FIF belon...
Ausführliche Beschreibung

In the present paper, the regularity of a Fractal Interpolation Function (FIF) is studied using wavelet transform. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation which FIF satisfies. By this method, it is shown that the FIF belongs to Lipschitz class of order , , under certain conditions on free parameters used in the construction of FIF. The second method is via Fourier transform of FIF. This approach gives the regularity of the FIF under certain conditions on free parameters. The Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform. Ausführliche Beschreibung