Helffer-Sj{\"o}strand formula for Unitary Operators
Aiman Mbarek (AGM)
TL;DR
This paper extends the Helffer-Sj{"o}strand formula, originally for self-adjoint operators, to unitary operators, providing a new analytical tool for spectral analysis of such operators.
Contribution
It introduces a novel formula for unitary operators analogous to the Helffer-Sj{"o}strand formula for self-adjoint operators.
Findings
Derived a Helffer-Sj{"o}strand type formula for unitary operators
Provides a new method for spectral analysis of unitary operators
Extends existing functional calculus techniques
Abstract
The objective of this paper to give a formula for unitary operators that corresponds to the Heler-Sj{\"o}strand formula for self-adjoint operators.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Matrix Theory and Algorithms · Quantum Mechanics and Non-Hermitian Physics