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Scaling of spectra of a class of self‐similar measures on R
Authors:Zhi‐Min Wang  Xin‐Han Dong  Wen‐Hui Ai
Abstract:Let urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0001 be two positive integers. For urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0002, let the self‐similar measure urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0003 be defined by urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0004. It is known 18] that urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0005 is a spectral measure with a spectrum urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0006 where urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0007. In this paper, we give some conditions on urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0008 under which the scaling set urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0009 is also a spectrum of urn:x-wiley:0025584X:media:mana201800360:mana201800360-math-0010.
Keywords:Fourier transform  scaling spectra  self‐similar measure  spectral measure  Primary: 28A80  Secondary: 42C05  46C05
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