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In the context of smooth interval maps, we study an inducing scheme approachto prove existence and uniqueness of equilibrium states for potentials $\phi$with he `bounded range' condition $\sup \phi - \inf \phi < \htop$, first usedby Hofbauer and Keller. We compare our results to Hofbauer and Keller's use ofPerron-Frobenius operators. We demonstrate that this `bounded range' conditionon the potential is important even if the potential is H\"older continuous. Wealso prove analyticity of the pressure in this context.

Equilibrium states for potentials with $\sup\phi - \inf\phi < \htop(f)$