Cauchy-Szegö integrals for systems of harmonic functions
We study the boundedness in of the projections onto spaces of functions with spectrum contained in horizontal strips. We obtain some results concerning convergence along nonisotropic regions of harmonic extensions of functions in with spectrum included in these horizontal strips.
We show that a harmonic function which vanishes continuously on an open set of the boundary of a convex domain cannot have a normal derivative which vanishes on a subset of positive surface measure. We also prove a similar result for caloric functions vanishing on the lateral boundary of a convex cylinder.