NON-SPECTRAL PROBLEM ON INFINITE BERNOULLI CONVOLUTION

作者：Li, Q.; Wu, Z-Y^*

来源：Analysis Mathematica, 2021, 47(2): 343-355.

DOI：10.1007/s10476-021-0069-7

• infinite Bernoulli convolution
• spectral measure
• orthogonal exponential functions
• Fourier transform

Let {d(k)}(k=1)(infinity) be an upper-bounded sequence of positive integers and let dE be the uniformly discrete probability measure on the finite set E. For 0 < rho < 1, the infinite convolution mu(rho),{0, d(k)} := delta(rho{0,d1}) * delta(rho 2{0,d2}) * ... is called an infinite Bernoulli convolution. The non-spectral problem on mu(rho,{0,dk}) is to investigate the cardinality of orthogonal exponentials in L-2(mu(rho,{0,dk})). In this paper, we give a characterization of this problem by classifying the values of rho.

• 单位
  中山大学