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MR284877 (44 #2101) 47.70 (39.00)
Karapetjanc, N. K.; Samko, S. G. The functional equation $\psi (x+\alpha )-b(x) \psi (x)=g(x)$. (Russian) Izv. Akad. Nauk Armjan. SSR Ser. Mat. 5 1970 no. 5, 441--448.
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