Asymptotic Expansions for Fourier Transform of Singular Self-Affine Measures
Asymptotic Expansions for Fourier Transform of Singular Self-Affine Measures
复制标题
奇异自仿射测度的傅里叶变换的渐近展开式
DOI：
10.1006/jmaa.1994.1355
复制
发表时间：
1994
期刊：
影响因子：
--
通讯作者：
K. Makarov
中科院分区：
文献类型：
--
作者：
K. Makarov
摘要研究了一类由轴上有限组仿射压缩生成的随机动力系统的奇异连续自仿射不变测度。计算了它们的支撑项和先导项的Hausdorff维数以及相应截断特征函数的L 2范数渐近项。结果表明，这些项的截断参数的对数的某些振荡函数乘以这些项的幂律行为是典型的。讨论了由不变测度特征函数的高频行为反重建不变测度的问题。
Abstract Singular continuous self-affine measures invariant with respect to some stochastic dynamical systems generated by a finite set of affine contractions on the axis are studied. The Hausdorff dimension of their support and leading terms of L 2 -norm asymptotic of the corresponding cut-off characteristic function are computed. It is shown that the power-law behavior multiplied by some oscillating functions of a logarithm of a cut-off parameter for these terms is typical. The inverse reconstruction problem of the invariant measure from the high-frequency behavior of its characteristic function is discussed.