Riemann-Birkhoff factorization/decomposition is a realization of a holomorphic matrix function of a circle as a product of a matrix holomorphic on a neighborhood of closed disk and a function of a matrix holomorphic on a neighborhood of an exterior of the disk including infinity and the circle itself. This decomposition is in the essence of Riemann-Hilbert problem. The interpretation in terms of loop groups is related to Bruhat decomposition.
There is an algebraic Birkhoff decomposition discovered in the study of Connes-Kreimer Hopf algebraic approach to renormalization in QFT.
Related Lab entries: loop group, Riemann-Hilbert problem, Wiener-Hopf decomposition
Last revised on August 30, 2024 at 09:16:37. See the history of this page for a list of all contributions to it.