Regularity of loop group factorization

Abstract

In the factorization of a Gl ⁡ ( n , C ) \operatorname {Gl}(n,\mathbb {C}) -valued loop φ \varphi into a unitary factor and a factor holomorphic in the disk, it is shown that the two factors each have as much regularity as φ \varphi , measured in a variety of function spaces, though with exceptions. This is analogous to known results for Birkhoff factorization, but somewhat different techniques are involved.