The $S$-resolvent estimates for the Spinor Dirac operator on manifolds with boundary conditions

Ivan Beschastnyi; Fabrizio Colombo; Simao Andrade Lucas; Irene Sabadini

The $S$-resolvent estimates for the Spinor Dirac operator on manifolds with boundary conditions

Spectral Theory 2026-06-30 v1

Authors: Ivan Beschastnyi , Fabrizio Colombo , Simao Andrade Lucas , Irene Sabadini

Abstract

The aim of this paper is to show that the spectral theory based on the S-spectrum is particularly well suited for the Dirac operator on manifolds, even in cases where the operator is not self adjoint. Traditionally, for non-self adjoint operators in the Clifford setting, the literature has often referred to the right spectrum. However, a more comprehensive approach is provided by the theory of the $S$ -spectrum, which is the appropriate notion for general operators on Clifford modules. In this work, we show that this theory is particularly well suited for bisectorial Clifford operators. By using the $S$ -spectrum, which naturally contains the right eigenvalues, we prove bisectorial estimates for the $S$ -resolvent associated with the spinor Dirac operator under various boundary conditions.

Keywords

S-spectrum Dirac operator bisectorial operators S-resolvent estimates Clifford modules boundary conditions

Cite

@article{arxiv.2606.31328,
  title  = {The $S$-resolvent estimates for the Spinor Dirac operator on manifolds with boundary conditions},
  author = {Ivan Beschastnyi and Fabrizio Colombo and Simao Andrade Lucas and Irene Sabadini},
  journal= {arXiv preprint arXiv:2606.31328},
  year   = {2026}
}