A necessary and sufficient condition for a two-sided continuous function to be cohomologous to a one-sided continuous function (vol 18, pg 131, 2003)

If (T) over cap : (X) over cap --> (X) over cap is a two-sided subshift on a finite number of symbols and T : X --> X is the corresponding one-sided subshift we give a necessary and sufficient condition for a continuous function (f) over cap : (X) over cap --> R to be cohomologous, with respect to ((X) over cap, (T) over cap), to a continuous function which can be defined on X. The property of being cohomologous to such a 'one-sided' function is important in the study of equilibrium states because there are extra tools, such as the Ruelle transfer operator, for one-sided systems. We present the results in the more general context when T : X --> X is a continuous surjection of a compact metric space and (T) over cap: (X) over cap --> (X) over cap is its natural extension, and look at the special case of subshifts. We also prove some related results and give applications to subshifts.