Localization properties of wavelet transforms. (English) Zbl 0778.42027

Summary: Estimates are given of the localization of wavelet transforms on the half-plane in terms of the localization of the analyzed function in time and frequency. Then a precise formulation of the wavelet analysis of tempered distributions is given. The results in this paper are well-known to the wavelet community. However, they are nowhere explicitly written up though they are quite useful. This paper therefore serves as reference for these kinds of results.


42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
46F10 Operations with distributions and generalized functions
Full Text: DOI


[1] DOI: 10.1063/1.526761 · Zbl 0571.22021
[2] Holschneider M., Inventiones Mathematicae 105 pp 15–
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