In this article, matrix-valued functions nonregular on the convex hull of the spectrum are considered. The logarithm, root and meromorphic functions of various matrices are examples of such functions. Here sharp norm estimates are established for the considered matrix-valued functions. Applications of the obtained estimates to the periodic problem and two-points boundary value problem for vector differential equations are also discussed.
- matrix-valued functions
- nonregular matrix functions
- periodic problem
- two-points boundary value problem
- vector differential equations