科研之友
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摘要
Let M = (.-1 0 0.-1) be an expanding real matrix with 0 <. < 1, and let D n = {( 00), ( sn 0), ( 0.n)} be digit sets with sn,.n. {-1, 1} for each n = 1. Then the infinite convolution mu M,{Dn} = dM- 1D1 * dM- 2D2 * center dot center dot center dot is called a Moran-Sierpinski measure. We give a necessary and sufficient condition for L2( mu M,{Dn}) to admit an infinite orthogonal set of exponential functions. Furthermore, we give the exact cardinality of orthogonal exponential functions in L2( mu M,{Dn}) when L2( mu M,{Dn}) does not admit any infinite orthogonal set of exponential functions based on whether. is a trinomial number or not.
