On Local Properties of Compactly Supported Solutions of the Two-coefficient Dilation Equation
نویسنده
چکیده
Let a and b be reals. We consider the compactly supported solutions φ :R→R of the twocoefficient dilation equation φ(x) = aφ(2x)+bφ(2x−1). In this paper, we determine sets Ba,b , Ca,b , and Za,b defined in the following way: let x ∈ [0,1]. We say that x ∈ Ba,b (resp., x ∈ Ca,b , x ∈ Za,b) if the zero function is the only compactly supported solution of the two-coefficient dilation equation, which is bounded in a neighbourhood of x (resp., continuous at x, vanishes in a neighbourhood of x). We also give the structure of the general compactly supported solution of the two-coefficient dilation equation.
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تاریخ انتشار 2002