期刊论文

He, Xing-Gang

英文

Advances in Mathematics

0001-8708

2014

259

511-531

10.1016/j.aim.2014.03.026

The research is partially supported by the RGC grant of Hong Kong and by the NNSF of China (Nos. 11371383 , 11271148 , 11171100 and 11371382 ), and the first author is also supported by the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-Sen University.

本校为通讯机构

For 0 < rho < 1 and N > 1 an integer, let mu be the self-similar measure defined by mu(center dot) = Sigma(N-1)(i=0) 1/N mu(rho(-1)(center dot) - i). We prove that L-2(mu) has an exponential orthonormal basis if and only if rho = 1/q for some q > 0 and N divides q. The special case is the Cantor measure with rho = 1/2k and N = 2 [16], which was proved recently to be the only spectral measure among the Bernoulli convolutions with 0 < rho < ...