Abstract:
Systems of dyadic wavelets on the positive half-line $\mathbb R_+$
equipped with the operation of binary summation are studied.
Several problems concerning approximation properties of
such wavelets are solved. In particular, explicit formulae
for the order of approximation of smooth functions and of binary-smooth
functions on $\mathbb R_+$ (smooth in the dyadic metric on the
binary half-line) are obtained. The dyadic approximations with
best approximation properties are characterized. The relation
between the smoothness of wavelets and their order of approximation is
analysed in various function spaces.
Bibliography: 24 titles.
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