Speaker: Dr. Vern Paulsen

Title: Factorization and Reproducing Kernel Hilbert Spaces

Abstract:  A classic algorithm of Cholesky provides the simplest way to test if a matrix is positive semidefinite while at the same time providing an LU-factorization(lower-upper). This algorithm also converges to provide an LU-factorization of operators on a Hilbert space with basis indexed by the natural numbers. However, problems in function theory seek UL-factorizations and these are known to not always exist.

  In this talk we will show how RKHS methods give necessary and sufficient conditions for factorizations to exist, even in multivariable cases where the function theory is not understood.