Abstract
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 ak for a special Laplace type second-order operator.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
