Heat content asymptotics for operators of Laplace type with spectral boundary conditions

TL;DR

This paper investigates the asymptotic behavior of heat content coefficients for Laplace-type operators with spectral boundary conditions, providing insights into their spectral properties and boundary effects.

Contribution

It introduces new analysis of heat content asymptotics for Laplace-type operators under spectral boundary conditions, extending previous understanding in spectral geometry.

Findings

Derived explicit formulas for heat content coefficients

Analyzed the influence of spectral boundary conditions on heat asymptotics

Provided new theoretical insights into boundary effects on heat content

Abstract

Let $P$ be an operator of Dirac type and let $D=P^2$ be the associated operator of Laplace type. We impose spectral boundary conditions and study the leading heat content coefficients for $D$.