Heat Equation Asymptotics of Elliptic Operators with Non‐scalar Leading Symbol

Let M be a compact smoot Riemannian manifold without boundary and let D = ad 0 δ 0 + b δ 1 d 1 – E on the space of smooth sections of the cotangent bundle where a and b are positive constants and where E is an endomorphism. We use functorial methods and the pseudo‐differential operator calculus to compute the quadratic term a 4 ( D ) in the asymptotic expansion of the heat equation trace.