Endomorphisms, transfer operators and Hilbert modules

这个项目是泛函分析的一般领域，纽卡斯尔大学和新南威尔士大学在这个领域都有很强的国际声誉。该项目的目的是研究转移算子存在时的不可逆动力学，正如Exel教授最近介绍的那样。动机来自于数学不同领域出现的各种例子，包括数论和图论。希望这些结果能对逼近理论和傅里叶分析中使用的多分辨分析背后的代数和解析结构有新的理解。该项目将有助于确保澳大利亚在数学方面拥有坚实的基础，这将促进创新。

This project is in the general area of functional analysis, an area where both Newcastle University and the University of New South Wales have strong international reputations. The aim of the project is to study irreversible dynamics in the presence of transfer operators, as recently introduced by Professor Exel. The motivation comes from a variety of examples arising in different areas of mathematics, including number theory and graph theory. It is hoped that the results will give new understanding of the algebraic and analytic structure underlying the multi-resolution analyses used in approximation theory and Fourier analysis. This project will help ensure that Australia has a strong foundation in mathematics which will foster innovation.