Approximation of Gaussian by Scaling Functions and Biorthogonal Scaling Polynomials

These relationships between the Gaussian and the Hermite polynomials are useful in linear scale-space analysis and applications to human and machine vision and image processing. The main objective of this paper is to extend these properties to a family of scaling functions that approximate the Gaussian function and to construct a family of Appell sequences of scaling biorthogonal polynomials that approximate the Hermite polynomials.