Dyadic wavelets and refinable functions on a half-lineстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:For an arbitrary positive integer n refinable functions on the positive half-line R_+ are defined, with masks that are Walsh polynomials of order 2^n-1. The Strang-Fix conditions, the partition of unity property, the linear independence, the stability, and the orthonormality of integer translates of a solution of the corresponding refinement equations are studied. Necessary and sufficient conditions ensuring that these solutions generate multiresolution analysis in L_2(R_+) are deduced. This characterizes all systems of dyadic compactly supported wavelets on R_+ and gives one an algorithm for the construction of such systems. A method for finding estimates for the exponents of regularity of refinable functions is presented, which leads to sharp estimates in the case of small n. In particular, all the dyadic entire compactly supported refinable functions on R_+ are characterized. It is shown that a refinable function is either dyadic entire or has a finite exponent of regularity, which, moreover, has effective upper estimates.