Bogoliubov Lab. of Theoretical Physics,
Joint Institute for Nuclear Research,
141980 Dubna, Moscow Region, RUSSIA

Heat kernel expansion for the dielectric like spectral problems

The heat kernel coefficients for scalar field obeying dielectric like matching conditions on an arbitrary interface are calculated with making use of potential theory for parabolic operators. The problem is formulated in terms of iteratively solvable system of integral equations  leading to a generalization of the known multiple reflection expansion. The coefficients are expressed through geometrical invariants of the interface.