Method for determining partial indices of symmetric matrix functions

摘要

A method for determining the partial indices of a matrix function that has a certain symmetry property is proposed. The method proposed is used to derive new effective sufficient conditions for the existence of a canonical factorization in the symmetric classes of unitary, Hermitian, orthogonal, circular, and symmetric matrix functions. The matrix G(x) is found to have a standard factorization. A matrix function that has symmetry property is considered and it is proved that there exist an operator that acts on the factorization of the matrix function. A boundary value problem of determining functions from a boundary condition specified on a contour coinciding with R is also considered.