TY - JOUR
T1 - Dimensions of non-differentiability points of generalized cantor functions
AU - Baek, In Soo
AU - Li, Wen Xia
N1 - Publisher Copyright:
©, 2014, Chinese Academy of Sciences. All right reserved.
PY - 2014/9/1
Y1 - 2014/9/1
N2 - For a probability vector p = (p1, ⋯, pN), there is a corresponding selfsimilar measure γp supported on the generalized Cantor set K in R generated by the family {hk(x) = akx + bk, k = 1, ⋯,N} (N ≥ 2) of contractive similitudes satisfying the strong separation condition. We consider the generalized Cantor function f(x) =γp([0, x] ∩ K) satisfying min[Formula is presented] on the unit interval. The numbers q+β(q) and ξ, where β'(q) =-1 with[Formula is presented], and [Formula is presented] give full information for the dimensions of the non-differentiability points and the null differentiability points and the infinity differentiability points of K.
AB - For a probability vector p = (p1, ⋯, pN), there is a corresponding selfsimilar measure γp supported on the generalized Cantor set K in R generated by the family {hk(x) = akx + bk, k = 1, ⋯,N} (N ≥ 2) of contractive similitudes satisfying the strong separation condition. We consider the generalized Cantor function f(x) =γp([0, x] ∩ K) satisfying min[Formula is presented] on the unit interval. The numbers q+β(q) and ξ, where β'(q) =-1 with[Formula is presented], and [Formula is presented] give full information for the dimensions of the non-differentiability points and the null differentiability points and the infinity differentiability points of K.
KW - Generalized Cantor function
KW - Non-differentiability point
KW - Self-similar measure
UR - https://www.scopus.com/pages/publications/84912050877
M3 - 文章
AN - SCOPUS:84912050877
SN - 0583-1431
VL - 57
SP - 939
EP - 946
JO - Acta Mathematica Sinica, Chinese Series
JF - Acta Mathematica Sinica, Chinese Series
IS - 5
ER -