On analytic injective matrix functions

Ela Analytic Roots of Invertible Matrix Functions∗

Various conditions are developed that guarantee existence of analytic roots of a given analytic matrix function with invertible values defined on a simply connected domain.

Analytic roots of invertible matrix functions

Various conditions are developed that guarantee existence of analytic roots of a given analytic matrix function with invertible values defined on a simply connected domain.

Analytic Approximation of Matrix Functions in L

We consider the problem of approximation of matrix functions of class L on the unit circle by matrix functions analytic in the unit disk in the norm of L, 2 ≤ p < ∞. For an m × n matrix function Φ in L, we consider the Hankel operator HΦ : H(C) → H −(C), 1/p + 1/q = 1/2. It turns out that the space of m × n matrix functions in L splits into two subclasses: the set of respectable matrix function...

Analytic Approximation of Matrix Functions and Dual Extremal Functions

We study the question of the existence of a dual extremal function for a bounded matrix function on the unit circle in connection with the problem of approximation by analytic matrix functions. We characterize the class of matrix functions, for which a dual extremal function exists in terms of the existence of a maximizing vector of the corresponding Hankel operator and in terms of certain spec...

Nevanlinna on Analytic Functions