
Nonspectrality of some selfaffine measures under the similarity in space
 QIN Ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2):
2332.
doi:10.6040/j.issn.16719352.0.2019.509

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The spectrality or nonspectrality of the selfaffine measure μ_{M,D} corresponding to matrix M=diag［p_{1}, p_{2}, p_{3}］ and the digit set D={0, e_{}1, e_{}2, e_{}3} has had many conclusions with previous researching, where p_{}1, p_{}2, p_{}3∈Z\{0, ±1}, e_{1}, e_{2}, e_{3} are the standard basis of unit column vectors in R^{3}. For the expanding integer matrix M=［p_{1}, p_{2}, p_{3}; p_{4}, p_{5}, p_{6}; p_{7}, p_{8}, p_{9}］ and the digit set D={0, e_{}1, e_{}2, e_{}3}, a method is presented here to deal with the nonspectrality of μ_{M,D}. As an application, the nonspectrality of a class of such selfaffine measures are clarified.