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Consider a function the following spaces: $$ \{f : \|(i\omega)k \hat f(\omega)\|_p ≤ 1, k ∈ N ∪ 0, p ∈ (1, ∞)\}. $$

Denote by $ \psi^m_D$ an orthonormal Daubechies wavelet of order m. One can find an that the extreme values of Daubechies wavelet coefficients for the above function spaces, i.e $$ A ≤ \|k(\hat \psi^m_D)\|_p ≤ B. $$

Where I can find applications of the above result?

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  • $\begingroup$ What's the link with Shannon entropy? $\endgroup$ – kodlu Jan 22 at 23:14
  • $\begingroup$ For example in neurocomputing: Application of wavelet energy and Shannon entropy for feature extraction in gearbox fault detection under varying speed conditions $\endgroup$ – user124297 Jan 23 at 3:58

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