On the mathematical properties of distributed approximating functionals

Abstract

This work investigates some mathematical properties of the Distributed Approximating Functionals (DAFs). We prove that certain classes of DAFs yield Unity Approximations. Two distinct classes which serve as examples are the Hermite-DAFs and the Sinc-class DAFs. Detailed proofs are given. A wavelet generator is constructed using the Continuous Wavelet Transform with repect to the scale parameter. Taking the Gaussian function as the scaling function, a numerical experiment is carried out demonstrating the use of the resulting wavelet for edge detection.