论文标题
Sierpiński垫圈和其他分形曲线上光谱三元的度量近似
Metric Approximations of Spectral Triples on the Sierpiński Gasket and other fractal curves
论文作者
论文摘要
非交通性几何形状通过构造光谱三元组提供了一个框架，以研究某些类别分形的几何形状。许多分形被构造为具有更简单结构的某些集合的自然限制：例如，sierpiński是由有限图组成的有限图的限制，该图由各种等边三角形的仿射图像组成。因此，自然要询问在一类称为分段的分形上构建的频谱三元组是否在适当意义上是在近似集合上的光谱三元组的限制。我们在本文中肯定地回答了这个问题，在本文中，我们在公制光谱三元组上使用光谱的前景，以使频谱三元组的迎接融合正式。我们的结果和方法与分形分析的研究有关，并具有潜在的物理应用。
Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed as natural limits of certain sets with a simpler structure: for instance, the Sierpiński is the limit of finite graphs consisting of various affine images of an equilateral triangle. It is thus natural to ask whether the spectral triples, constructed on a class of fractals called piecewise $C^1$-fractal curves, are indeed limits, in an appropriate sense, of spectral triples on the approximating sets. We answer this question affirmatively in this paper, where we use the spectral propinquity on the class of metric spectral triples, in order to formalize the sought-after convergence of spectral triples. Our results and methods are relevant to the study of analysis on fractals and have potential physical applications.
