Symbolic computation of DeWitt-Seeley-Gilkey coefficients on curved manifolds
Let \(M\) be an \(n\)-dimensional compact curved manifold with a torsion and let \(A\) be a positive elliptic differential operator of order \(2r\) on \(M\). Consider the asymptotic expansion, \(\langle x \mid e^{-tA} x \rangle \sim \sum E_ m(x | A) t^{(m - n)/2r}\), \(m \geq 0\), \(t \to +0\). The functions \(E_ m\) are called DeWitt-Seely-Gilkey coefficients. Using the Widom covariant symbolic calculus for pseudodifferential operators, the authors give an algorithm of computing the coefficients \(E_ m\). Some examples are provided.
scientific article; zbMATH DE number 638320