Fourier Orthonormal Bases of Two Dimensional Moran Measures with Four-Element Digits

摘要

Let mu({Mn}, {Dn}) be a Moran measure generated by {(M-n, D-n)}(n=1)(infinity), where M-n = @@@ [GRAPHICS] @@@ is an element of M-2(Z) is an expanding matrix and D-n = { @@@ [GRAPHICS] @@@ , @@@ [GRAPHICS] @@@ , @@@ [GRAPHICS] @@@ , @@@ [GRAPHICS] @@@ } subset of Z(2) is a finite digit set. In the present paper we will study the problem of how to determine the Hilbert space L-2(mu({Mn},{Dn})) has a Fourier basis. We first obtain a sufficient condition for this aim and give some examples to explain the theory. Moreover, we completely settle the corresponding problem if a(n) = b(n) = 1 for all n >= 1.

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