The Higher Dimensional Hermite Transform: A New Approach

In this article we expand the filter functions of the classical Hermite transform into the Clifford-Hermite polynomials. Furthermore, we construct a new higher dimensional Hermite transform within the framework of Clifford analysis using the radial and generalized Clifford-Hermite polynomials. Finally we compare this newly introduced Clifford-Hermite transform with the Clifford-Hermite Continuous Wavelet transform.