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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.

MSC:

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

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