Growth of heat trace and heat content asymptotic coefficients

TL;DR

This paper investigates the growth behavior of heat trace and heat content asymptotic coefficients, demonstrating unbounded growth in smooth cases but establishing universal bounds in real analytic contexts.

Contribution

It reveals the contrasting growth properties of heat asymptotics in smooth versus real analytic settings, providing new bounds and growth criteria.

Findings

Unbounded growth of heat asymptotics in smooth categories.

Universal bounds on heat asymptotics in real analytic categories.

Differentiation between smooth and real analytic cases.

Abstract

We show in the smooth category that the heat trace asymptotics and the heat content asymptotics can be made to grow arbitrarily rapidly. In the real analytic context, however, this is not true and we establish universal bounds on their growth.