Abstract
Let 0<|ρ|<1 and I2 be the 2×2 identical matrix. For an expanding real matrix M=ρ−1I2∈M2(R) and a four-element digit set D={(0,0)t,(1,0)t,(0,1)t,(−1,−1)t}⊂Z2 with cardinality |D|, let μM,D be the self-affine measure defined by μM,D(⋅)=1|D|∑d∈DμM,D(M(⋅)−d). In this paper, we prove that L2(μM,D) has an exponential orthonormal basis if and only if ρ−1∈2Z∖{0}.
Published Version
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