Piecewise harmonic subharmonic functions and positive Cauchy transforms
Piecewise harmonic subharmonic functions and positive Cauchy transforms
We give a local characterization of the class of functions having positive distributional derivative with respect to z that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild nondegeneracy assumptions.As a consequence, we give conditions that guarantee that any subharmonic piecewise harmonic function coincides …