The Spectra on Lie Groups and Its Application to twisted L2-Invariants

by Zhicheng Han
Doctoral thesis
Date of Examination:2023-09-14
Date of issue:2024-02-29
Advisor:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Thomas Schick
Referee:Prof. Dr. Ralf Meyer
Persistent Address: http://dx.doi.org/10.53846/goediss-10360

 

 

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Abstract

English

We computed spectra of various $G$-invariant differential operators on the universal cover of 2x2 unimodular groups. This was achieved by applying tools from harmonic analysis/representation theory to corresponding groups. In this thesis we have discussed in detail how to apply harmonic analysis to study such problems, this include in particular a detailed analysis of the operator in question, a estimate of the growth of its kernel, and later the computation of the spectra for several operators. Towards the second half we applied the data to compute the Novikov-Shubin invariants on respective group, which is a topological invariant defined to measure the heat decay at large time.
Keywords: L2-invariants; Novikov-Shubin invariants; Lie groups; Harmonic analysis
 
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