Asymptotic expansions for the heat content
Let \(\beta\) be a bounded operator and \(B_\beta\) the operator satisfying the boundary operator condition determined by \(\beta f=0.\) The author uses spectral theory to express the heat content in terms of the spectral resolution of the operator \(B_\beta\) and to relate the asymptotics with a suitably modified zeta function. Then it is shown how the Mellin transform and the properties of the zeta function can be used to obtain the heat content asymptotics for a generalized heat operator. The author introduces the heat content on the boundary and develops some of its properties. She also computes the asymptotics for the boundary invariant when \(B_\beta\) is an operator of Laplace type with Dirichlet and Neumann boundary conditions. Using the above results it is possible to compute the generalized heat content asymptotics for an operator of Dirac type.
scientific article; zbMATH DE number 1344246