Time-dependent operators on some non-orientable projective orbifolds

摘要

In this paper, we present an explicit construction for the fundamental solution of the heat operator, the Schrodinger operator, and related first-order parabolic Dirac operators on a class of some conformally flat non-orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds. Copyright (C) 2015 JohnWiley & Sons, Ltd.