Approximations Using Hilbert Transform of Wavelets
نویسندگان
چکیده
Hilbert transform of wavelets has been used to approximate functions in L2(R) . It is proved that Hilbert transform of wavelets with many vanishing moments does a good job in approximating smooth functions in L2(R) . We also prove that Hölder continuity of a function helps in the decay of wavelet coefficients and thereby helps in approximating it. Finally, we give a result that relates the Hilbert transform of wavelet with dyadic scale differential operator and use it to decrease the wavelet coefficients. Mathematics subject classification (2010): 44A15, 42A38, 65T60, 41A35.
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