On the relation between determinants and Green functions of elliptic operators with local boundary conditions
Horacio Alberto Falomir, Ricardo Enrique Gamboa Saravi, Mar\'{\I}a, Amelia Muschietti, Eve Mariel Santangelo, Jorge Eduardo Solomin
TL;DR
This paper presents a formula linking the ratios of determinants of elliptic differential operators with local boundary conditions to their Green functions, enhancing understanding of their spectral properties.
Contribution
It introduces a novel formula connecting determinants and Green functions for elliptic operators with local boundary conditions.
Findings
Derived a formula relating determinants and Green functions.
Established the connection for operators sharing the same principal symbol.
Provides a tool for spectral analysis of elliptic operators.
Abstract
A formula relating quotients of determinants of elliptic differential operators sharing their principal symbol, with local boundary conditions, to the corresponding Green function is given.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems