The computational power of infinite time Blum–Shub–Smale machines

Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM) are characterized via iterated Turing jumps, and we propose a normal form for these functions. It is also proved that the set of ITBM computable reals coincides with $\mathbb R\cap L_{\omega^\omega}$.