Existence de “fonction-père” pour les ondelettes à support compact. (Existence of father functions for compactly supported wavelets). (French) Zbl 0752.42017

Lemarié-Rieusset, Pierre-Gilles

C. R. Acad. Sci., Paris, Sér. I 314, No. 1, 17-19 (1992).

Summary: We show that a wavelet basis \((\psi_{j,k})\) of \(L^ 2(\mathbb{R})\) with a Hölderian and compactly supported “mother function” \(\psi\) always results by a multi-resolution analysis. The “father function” \(\varphi\) has the same regularity as \(\psi\) and can be chosen with compact support.

MSC:

42C40	Nontrigonometric harmonic analysis involving wavelets and other special systems
46B15	Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces

Keywords:

ondelettes; wavelet basis; mother function; multi-resolution analysis; father function; compact support