Extension of Case formulas to L_p. Application to half and full space problems

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 X p = {f‖μf (μ) ‐ L p }, where the expansions are now to be interpreted in the X p norm. The spectral family for the transport operator is then obtained explicitly, and is used to solve transport problems with X p sources and incident distributions.