Holder continuity of the spectral measures for one-dimensional Schrodinger operator in exponential regime Academic Article uri icon


  • Avila and Jitomirskaya prove that the spectral measure v,,xf of quasi-periodic Schrdinger operator is 1/2-Hlder continuous with appropriate initial vector f, if satisfies Diophantine condition and is small. In the present paper, the conclusion is extended to that for all with () > , the spectral measure v,,xf is 1/2-Hlder continuous with small , if v is real analytic in a neighbor of {xC}, where C is a large absolute constant. In particular, the spectral measure ,,xf of almost Mathieu operator is 1/2-Hlder continuous if >eC with C a large absolute constant.

published proceedings


author list (cited authors)

  • Liu, W., & Yuan, X.

citation count

  • 4

complete list of authors

  • Liu, Wencai||Yuan, Xiaoping

publication date

  • January 2015