Abstract
This work presents an analysis of the reproducing kernel K(p) associated to a class of wavelets K(p) derived from the theory of multiplicatively advanced differential equations. These kernels K(p) are expressible in terms of a family of new wavelets fk(t), which are generated by two fundamental wavelets Cosq(t) and Sinq(t), all of which satisfy multiplicatively q-advanced perturbations of the second-order equation of the harmonic oscillator f″(t)=−f(t). As the parameter q→1+, Cosq(t) and Sinq(t) approach cos(t) and sin(t) uniformly, respectively, on compact subsets of R. Decay rates for K(p) as q→∞ are given, refining the understanding of the associated frame operator S, and providing for efficiency in inversion of S.
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