Spectral asymptotics and regularized traces for Dirac operators on a star-shaped graph

Abstract

In this article, we consider the spectral problems for Dirac operators on a star-shaped graph. First, we derive the asymptotic expressions of the eigenvalues and then explicitly establish the regularized trace formulae for the operators in terms of the coefficients of the operators.

Keywords:

• Dirac operator
• star-shaped graph
• trace formula

AMS Subject Classifications::

• 34B45
• 34L15
• 34L40

Acknowledgements

The authors thank the referees for valuable comments. This work was supported by Natural Science Foundation of Jiangsu Province of China (BK 2010489) and the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366), and NUST Research Funding (No. AE88787).