Asymptotic expansions of the wavelet transform in \({\mathbb R}^n\) (Q2798873)

The author studies moment asymptotic expansions and asymptotic expansions of \(n\)-dimensional wavelet transforms. He recalls definitions and properties of test functions and generalized functions used by \textit{R. Estrada} and \textit{R. P. Kanwal} [Proc. R. Soc. Lond., Ser. A 428, No. 1875, 399--430 (1990; Zbl 0717.46034); J. Math. Anal. Appl. 163, No. 1, 264--283 (1992; Zbl 0764.41029)]. The paper is organized as follows: In Section 1 the author recalls some basic definitions and notations of wavelet transforms in \(n\)-dimensions and asymptotic expansions of functions. Section 2 presents two moment asymptotic expansions of the wavelet transform in \({\mathbb R}^n\). Section 3 studies asymptotic expansions of the wavelet transform in \({\mathbb R}^n\) with explicit error bound. Finally, Section 4 gives some examples of asymptotic expansions, especially, for the Morlet wavelet transform and the Haar wavelet transform.