Spectral Theory of Dirac Operators

TL;DR

This paper provides a comprehensive overview of the spectral theory of Dirac operators, covering transformation operators, eigenvalue asymptotics, self-adjoint extensions, eigenfunction expansions, inverse problems, and isospectral operators.

Contribution

It offers a detailed synthesis of key topics in Dirac operator spectral theory, including new insights into inverse problems and isospectrality.

Findings

Analysis of transformation operators and eigenvalue asymptotics

Development of inverse problem solutions for Dirac operators

Characterization of isospectral Dirac operators

Abstract

The main issues of the spectral theory of Dirac operators are presented, namely: transformation operators, asymptotics of eigenvalues and eigenfunctions, description of symmetric and self-adjoint operators in Hilbert space, expansion in eigenfunctions, uniqueness theorems in inverse problems, constructive solution of inverse problems, description of isospectral operators, and some other questions. This book is aimed at specialists in spectral theory and graduate students of mathematics at universities.