Dimensions of non-differentiability points of generalized cantor functions

In Soo Baek; Wen Xia Li

Dimensions of non-differentiability points of generalized cantor functions

In Soo Baek
, Wen Xia Li^*

^*Corresponding author for this work

School of Mathematical Sciences

Busan University of Foreign Studies

Research output: Contribution to journal › Article › peer-review

Abstract

For a probability vector p = (p1, ⋯, pN), there is a corresponding selfsimilar measure γ_p supported on the generalized Cantor set K in R generated by the family {h_k(x) = a_kx + b_k, k = 1, ⋯,N} (N ≥ 2) of contractive similitudes satisfying the strong separation condition. We consider the generalized Cantor function f(x) =γ_p([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.

Original language	English
Pages (from-to)	939-946
Number of pages	8
Journal	Acta Mathematica Sinica, Chinese Series
Volume	57
Issue number	5
State	Published - 1 Sep 2014

Keywords

Generalized Cantor function
Non-differentiability point
Self-similar measure

Cite this

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title = "Dimensions of non-differentiability points of generalized cantor functions",

abstract = "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.",

keywords = "Generalized Cantor function, Non-differentiability point, Self-similar measure",

author = "Baek, \{In Soo\} and Li, \{Wen Xia\}",

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TY - JOUR

T1 - Dimensions of non-differentiability points of generalized cantor functions

AU - Baek, In Soo

AU - Li, Wen Xia

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 -

Dimensions of non-differentiability points of generalized cantor functions

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