Spectral Property Of Self-similar Measures With Equal Difference Digits

We consider the iterated function system fk(x)=n-1(x+i),i=-b,0,b,2b,…,b(m-2)arises a self-similar measure μm,n with equal weight.Then the maximal orthogonal set is described by improving the maximal tree mapping,thus we can study spectral measure.In Chapter two,we first introduced the definition that we need to use in the pater and some basic knowledge.In Chapter three,we will give a necessary and sufficient condition for μm,n having infinitely many orthogonal exponentials.In particular,if m divides b,then μq,b is a spectral measure.In this way,we will give a necessary and sufficient condition for Γbeing the maximal orthogonal set.In Chapter four,we will give a proof of the spectral property of τ being not affected if we alter only elements △m={δ0∞:δ∈Φm*} in m-adic tree.