Positivity of refinable functions defined by nonnegative finite masks

Abstract: Let with be a given nonnegative mask. Assume that the subdivision scheme with this mask is convergent. Let the associated refinable function be ϕ. So the support of ϕ is contained in . Melkman conjectured in 1997 that unless the scheme is interpolatory and the refinable function ϕ is positive on . In the present paper we confirm this conjecture. A lower bound of ϕ on is also given. [Copyright &y& Elsevier]