ISSN:
0945-3245
Keywords:
AMS (MOS): 44 A15
;
65D99
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary We extend the continuous wavelet transform to Sobolev spacesH s(ℜ) for arbitrary reals and show that the transformed distribution lies in the fiber spaces $$L_2 \left( {\left( {\mathbb{R}_0 ,\frac{{da}}{{a^2 }}} \right),H^s \left( \mathbb{R} \right)} \right) \cong H^{0,s} \left( {\mathbb{R}^2 ,\frac{{dadb}}{{a^2 }}} \right)$$ . This generalisation of the wavelet transform naturally leads to a unitary operator between these spaces. Further the asymptotic behaviour of the transforms ofL 2-functions for small scaling parameters is examined. In special cases the wevelet transform converges to a generalized derivative of its argument. We also discuss the consequences for the discrete wavelet transform arising from this property. Numerical examples illustrate the main result.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01385659
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