论文信息 - Complete monotonicity of solutions of the Abel equation $F(e^x)=F(x)+1$

Complete monotonicity of solutions of the Abel equation $F(e^x)=F(x)+1$

Summary. We investigate the functions F : R → R which are C ∞ solutions of the Abel functional equation F ( e x ) = F ( x ) + 1 . In particular, we determine the asymptotic behaviour of the derivatives and show that no solution can have F ′ completely monotonic on any interval ( α, ∞ ) . We discuss what could be considered the best behaved solution of this equation.

T. Hilberdink

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