Extension of the truncated bi-indexed weighted shifts‎, ‎recursiveness and subnormality

Abstract

We build a process in order to extend the truncated weighted shift‎, ‎using techniques of the bi-indexed recursive sequences‎. ‎We apply this process to solve the subnormality of $2$-variable weighted shifts‎, ‎whose associated moment sequence is a bi-indexed recursive sequence‎. ‎Notably‎, ‎we detail the case of the truncated $2$-variable weighted shift $T\equiv(T_1‎, ‎T_2)$ of order $(2,2)$‎.