Invertibility properties of matrix wiener‐hopf plus Hankel integral operators

Abstract

We consider matrix Wiener‐Hopf plus Hankel operators acting between Lebesgue spaces on the real line with Fourier symbols presenting some even properties (which in particular include unitary matrix‐valued functions), and also with Fourier symbols which contain sectorial matrices. In both situations, different conditions are founded to ensure the operators invertibility, one‐sided invertibility, Fredholm property, and the so‐called n and d‐normal properties. An example is provided to illustrate the proposed theory.

Key words:

• matrix Wiener‐Hopf plus Hankel operator
• invertibility
• Fredholm property
• unitary matrix‐valued function
• sectorial matrix‐valued function