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Analysis Seminar - Scattering Systems and Agler Decompositions on the Bidisk

Kelly Bickel, Department of Mathematics, Washington University in St. Louis

April 8, 2013 - 4:00 pm to 5:00 pm
Location: Cupples I, Room 199 | Host: Prof. John McCarthy

Abstract: Given a general Schur function f on the bidisk, one can define an associated de Branges-Rovynak scattering system whose scattering function coincides with f. In this talk, we will discuss how known decompositions of the system's scattering subspace can be used to construct Agler decompositions of f, e.g., decompositions of f using pairs (A¹, A²) of positive kernels. These Agler decompositions have a particular structure, which implies certainly properties about the functions in the Hilbert spaces H(A¹) and H(A²). In particular, these properties can be used to obtain a characterization of when the functions in H(A¹) and H(A²) can be analytically continued across portions of the boundary of the bidisk.