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Completeness of elementary solutions of the transport equation for an exponential atmosphere

Journal Article · · Transp. Theory Stat. Phys.; (United States)

Previously reported elementary solutions of the linear transport equation for an exponential scattering ratio c(z) = c/sub 0/e/sup -z//s are shown to be complete on the range (-s/(s+1),1) provided c/sub 0/ and s satisfy a certain inequality; thus these eigenfunctions are incomplete on the full range (1,1). A new set of elementary solutions with larger spectrum is constructed and completeness is proved for the larger interval (-1,1)--but from which two certain subintervals of arbitrary small width have been deleted, again provided c/sub 0/ and a satisfy a certain inequality. Other half-range completeness questions are also addressed.

Research Organization:
School, Engineering and Applied Science, University of California, Los Angeles, California 90024
OSTI ID:
6044524
Journal Information:
Transp. Theory Stat. Phys.; (United States), Journal Name: Transp. Theory Stat. Phys.; (United States) Vol. 11:2; ISSN TTSPB
Country of Publication:
United States
Language:
English

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