Model-independent determination of the gap function of nearly localized superconductors

The gap function $\mathrm{\ensuremath{\Delta}}(\ensuremath{\omega})$ carries essential information on both, the pairing glue as well pair-breaking processes in a superconductor. Unfortunately, nearly localized superconductors with nonconstant density of states normal state, standard procedure for extraction cannot be applied. Here we introduce model-independent method that makes it possible to extract also this case. feasibility is demonstrated tunneling data disordered thin films TiN. We find an unconventional feature which suggests electrons TiN are coupled very soft mode.