%0 Journal Article
%T Green functions of higher-order differential operators
%A Ivan G. Avramidi
%J Mathematics
%D 1997
%I arXiv
%R 10.1063/1.532436
%X The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of higher-order operators formed by the products of second-order operators of Laplace type defined with the help of a unique Riemannian metric but with different bundle connections and potential terms. The asymptotic expansion of the Green functions near the diagonal is studied in detail in any dimension. As a by-product a simple criterion for the validity of the Huygens principle is obtained. It is shown that all the singularities as well as the non-analytic regular parts of the Green functions of such high-order operators are expressed in terms of the usual heat kernel coefficients $a_k$ for a special Laplace type second-order operator.
%U http://arxiv.org/abs/hep-th/9707040v2