Vector refinement equations with infinitely supported masks
نویسندگان
چکیده
منابع مشابه
Subdivision Schemes and Refinement Equations with Nonnegative Masks
We consider the two-scale refinement equation f(x) = ∑N n=0 cnf(2x − n) with ∑ n c2n = ∑ n c2n+1 = 1 where c0, cN 6= 0 and the corresponding subdivision scheme. We study the convergence of the subdivision scheme and the cascade algorithm when all cn ≥ 0. It has long been conjectured that under such an assumption the subdivision algorithm converge, as well as the cascade algorithm converge unifo...
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A compactly supported scaling function can come from a refinement equation with infinitely many nonzero coefficients (an infinite mask). In this case we prove that the symbol of the mask must have the special rational form ã(Z) = b̃(Z)c̃(Z)/b̃(Z). Any finite combination of the shifts of a refinable function will have such a mask, and will be refinable. We also study compactly supported solutions o...
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in this paper, we study l1 -solutions of the following two-direction poly-scale refinement equationwe prove that the vector space of all l1 -solutions of the above equation is at most one-dimensional andconsists of compactly supported functions of constant sign. we also show that any- l1 solution of the aboveequation is either positive or negative on its support under a special assumption. with...
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In this paper, we present a necessary and sufficient condition for the existence of solutions in a Sobolev space W k p (R)(1 6 p 6 ∞) to a vector refinement equation with a general dilation matrix. The criterion is constructive and can be implemented. Rate of convergence of vector cascade algorithms in a Sobolev space W k p (R) will be investigated. When the dilation matrix is isotropic, a char...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2007
ISSN: 0021-9045
DOI: 10.1016/j.jat.2007.03.004