HEAT KERNEL COEFFICIENTS OF THE LAPLACE OPERATOR ON THE D-DIMENSIONALBALL

We present a very quick and powerful method for the calculation of hea t kernel coefficients. It makes use of rather common ideas, as integra l representations of the spectral sum, Mellin transforms, non-trivial commutation of series and integrals and skillful analytic continuation of zeta functions on the complex plane. We apply our method to the ca se of the heat kernel expansion of the Laplace operator on a D-dimensi onal ball with either Dirichlet, Neumann or, in general, Robin boundar y conditions. The final formulas are quite simple. Using this case as an example, we illustrate in detail our scheme - which serves for the calculation of an (in principle) arbitrary number of heat kernel coeff icients in any situation when the basis functions are known. We provid e a complete list of new results for the coefficients B-3,..., B-10, c orresponding to the D-dimensional ball with all the mentioned boundary conditions and D = 3,4,5. (C) 1996 American Institute of Physics.