POSITIVE EXTENSIONS OF MATRIX FUNCTIONS OF TWO VARIABLES WITH SUPPORT IN AN INFINITE BAND

摘要

Let W~(n×n) denote the Wiener algebra of n × n matrix functions on the bitorus T~2 = T × T,rni.e., F(e~(it),e(iw))= ∞∑ k,l=- ∞ A_(kl)e~(ikt)e~(ilw) ∈ W~(n × n) if ∞∑ k,l=- ∞ ‖A_(kl)‖ < ∞, where A_(kl )are complex n × nrnmatrices, and where ‖X‖ denotes the operator norm of a matrix X. We let (L~2(T~2))~((n)) be the Hilbert space of n-component column vectors with components in L~2(T~2).