The reducibility of compressed shifts on a class of quotient modules over the bidisk

Abstract

In this paper, we show that, for the rational inner function θ(z,w)=zw+b¯w+c¯z+d¯1+bz+cw+dzw, Sz is reducible on the quotient module Kθ=H2⊖θH2 over the bidisk if and only if θ is the product of two one-variable inner functions.