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

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1975-05
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AIP Publishing
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 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.

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Larsen, E. W.; Sancaktar, S.; Zweifel, P. F., "Extension of Case formulas to L<sub>p</sub>. Application to half and full space problems," J. Math. Phys. 16, 1117 (1975); http://dx.doi.org/10.1063/1.522641