论文标题
有限自动化操作员的一些通用分形特性
Some generic fractal properties of bounded self-adjoint operators
论文作者
论文摘要
我们通过其光谱测量的下部和上部分形维度研究有界自动化算子的一般分形特性。提出了两组结果。首先，可以表明，相关光谱测量的矢量集具有较低（上）的广义分形尺寸，每$ q>> 1 $（$ 0 <q <1 $）等于零（一个）是空的。第二个给出了足够的条件，对于可分离的算子的可分分离空间，对于普通极端值的存在；在这种情况下，我们有一个新的证明著名的仙境定理。
We study generic fractal properties of bounded self-adjoint operators through lower and upper generalized fractal dimensions of their spectral measures. Two groups of results are presented. Firstly, it is shown that the set of vectors whose associated spectral measures have lower (upper) generalized fractal dimension equal to zero (one) for every $q>1$ ($0<q<1$) is either empty or generic. The second one gives sufficient conditions, for separable regular spaces of operators, for the presence of generic extreme dimensional values; in this context, we have a new proof of the celebrated Wonderland Theorem.
