November 19, 2012 -
4:00 pm to 5:00 pm
Location: Cupples I, Room 199 |
Host: Prof. John McCarthy
Abstract: It is well known that operator-valued inner functions on the bidisk admit decompositions in terms of two reproducing kernels, called Agler decompositions. In past talks, I have presented an elementary, constructive proof of the existence of such decompositions. In this talk, l will analyse the structure and regularity of the canonical decompositions and associated Hilbert spaces arising from the proof. These canonical decompositions can be used to characterize all Agler decompositions and provide a uniqueness criterion. Hence, several properties of the canonical decompositions can be extended to all Agler decompositions. Time permitting, I will also discuss results specific to rational inner functions and their decompositions. This is joint work with Greg Knese.
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