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