We study the propagation of microlocal analytic singularities for the microdifferential equations with conical refraction studied by R. Melrose and G. Uhlmann. We transform the equations to a simple canonical form 2-microlocaly through quantized bicanonical transformations by Y. Laurent.
Using a distributional approach to integration in superspace, we investigate a Cauchy-Pompeiu integral formula in super Dunkl-Clifford analysis and several related results, such as Stokes formula, Morera's theorem and Painlevé theorem for super Dunkl-monogenic functions. These results are nice generalizations of well-known facts in complex analysis.
denotes a (compact, nonsingular) lamination by hyperbolic Riemann surfaces. We prove that a probability measure on is harmonic if and only if it is the projection of a measure on the unit tangent bundle of which is invariant under both the geodesic and the horocycle flows.
Let be a principal fiber bundle and an associated fiber bundle. Our interest is to study the harmonic sections of the projection of into . Our first purpose is give a characterization of harmonic sections of into regarding its equivariant lift. The second purpose is to show a version of a Liouville theorem for harmonic sections of .