Diagonal short time asymptotics of heat kernels for certain degenerate second order differential operators of Hörmander type (Q1123309)

The author studies partial differential operators of the form \(L=(1/2)\sum^{n}_{i=1}\hat V^ 2_ i+\hat V_ 0\) where the \(\{\) \(\hat V_ j\}\) are vector fields which generate a Lie algebra of top dimension and \(V_ 0\) is not zero. The author studies the diagonal short time asymptotics for the Wiener functional of the associated heat equation \((\partial /\partial t-L)u=0\).