Theoretical Statistics and Mathematics Unit, ISI Delhi

August 22, 2012 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Srijanani Anurag Prasad,
Indian Statistical Institute, Delhi

Title:
Fourier Transform and Wavelet Transform of Fractal Interpolation Functions

Abstract of Talk

Fractal Interpolation Function is a new and novel method to construct irregular functions from interpolation data. In this talk, beginning with a brief introduction on
construction of Fractal Interpolation Function, we will discuss the Fourier transform
and Wavelet transform of the same. The wavelet transform of FIF is obtained through
two different methods. The first method is via Fourier transform of FIF. This approach
gives the $\lambda$-regularity, $(0 < \lambda)$, of FIF under certain conditions on free parameters. The second method uses the functional equation through which FIF is constructed. By this method, it is shown that the FIF belongs to Lipschitz class of order $\delta, (0 < \delta \leq 1)$, under certain conditions on free parameters.