Extension of the Case formulas to <i>L</i> <i>p</i>. Application to half and full space problems

Abstract

The singular eigenfunction expansions originally applied by Case to solutions of the transport equation are extended from the space of Hölder-continuous functions to the function spaces Xp = {f‖μf (μ) - Lp}, where the expansions are now to be interpreted in the Xp norm. The spectral family for the transport operator is then obtained explicitly, and is used to solve transport problems with Xp sources and incident distributions.