The generalized Hermitean Clifford‐Hermite continuous wavelet transform

The one‐dimensional continuous wavelet transform (CWT) is a successful tool in signal and image analysis, with numerous applications (see e.g. [8, 9]). Standard (or orthogonal) Clifford analysis is a higher dimensional function theory which has proven to constitute an appropriate framework for developing higher dimensional CWTs, where all dimensions are encompassed at once, as opposed to tensorial approaches with products of onehyp‐dimensional phenomena; the specific construction of higher dimensional wavelets is based on particular families of orthogonal polynomials, see e.g. [4, 5, 6, 7]. We explicitly mention the generalized Clifford‐Hermite polynomials, introduced in [10] and applied to wavelet analysis in [7]. More recently, Hermitean Clifford analysis has emerged as a new branch of Clifford analysis, refining the orthogonal case, see [1]. Hermitean Clifford‐Hermite polynomials and their associated families of wavelet kernels ! were constructed in [2, 3]. In this contribution, we introduce generalized Hermitean Clifford‐Hermite polynomials, involving in their definition Hermitean spherical monogenics, the ultimate goal being new generalized continuous wavelet transforms.