HEAT KERNEL-EXPANSION FOR OPERATORS CONTAINING A ROOT OF THE LAPLACE OPERATOR

We suggest a method for the calculation of the DeWitt-Seeley-Gilkey (D WSG) coefficients for the operator root-del(2) + V(x) basing on a gene ralization of the pseudodifferential operator technique. The lowest DW SG coefficients for this operator are calculated by using the method p roposed. We show that the problem of the calculation of the DWSG coeff icients for operators of the type (-del(2) + V(x))(1/q), where q is an arbitrary natural number, is solvable. Namely, we deduce an explicit formula expressing the DWSG coefficients for operators with the root t hrough the DWSG coefficients for operators without the root. (C) 1997 American Institute of Physics.