Abstract
We show that the scale-space operators defined by a class of refinable kernels satisfy a version of the causality property, and a sequence of such operators converges to the corresponding operator with the Gaussian kernel, if the sequence of refinable kernels converges to the Gaussian function. In addition, we consider discrete analogs of these operators and show that a class of refinable sequences satisfies a discrete version of the causality property. The solutions of the corresponding discrete refinement equations are also investigated in detail.
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Communicated by J. Carnicer and J.M. Peña
In commemoration of the sixtieth birthday of Mariano Gasca
Mathematics subject classifications (2000)
94A12, 47B38, 41A25, 7B37.
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Goh, S.S., Goodman, T.N.T. & Lee, S.L. Causality properties of refinable functions and sequences. Adv Comput Math 26, 231–250 (2007). https://doi.org/10.1007/s10444-004-8007-3
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DOI: https://doi.org/10.1007/s10444-004-8007-3