  We investigate theoretically, the character of electronic eigenstates and
transmission properties of a one dimensional array of stubs with Cantor
geometry. Within the framework of real space re-normalization group (RSRG) and
transfer matrix methods we analyze the resonant transmission and extended
wave-functions in a Cantor array of stubs, which lack translational order.
Apart from resonant states with high transmittance we unravel a whole family of
wave-functions supported by such an array clamped between two-infinite ordered
leads, which have an extended character in the RSRG scheme, but, for such
states the transmission coefficient across the lead-sample-lead structure
decays following a power-law as the system grows in size. This feature is
explained from renormalization group ideas and may lead to the possibility of
trapping of electronic, optical or acoustic waves in such hierarchical
geometries.
