JournalsjstVol. 11, No. 2pp. 847–872

Invertibility issues for a class of Wiener–Hopf plus Hankel operators

  • Victor D. Didenko

    Southern University of Science and Technology, Shenzhen, China
  • Bernd Silbermann

    Technische Universität Chemnitz, Germany
Invertibility issues for a class of Wiener–Hopf plus Hankel operators cover

This article is published open access under our Subscribe to Open model.

Abstract

The invertibility of Wiener–Hopf plus Hankel operators W(a)+H(b)W(a)+H(b) acting on the spaces Lp(R+)L^p(\mathbb{R}^+), 1p<1 \leq p<\infty is studied. If aa and bb belong to a subalgebra of L(R)L^\infty(\mathbb{R}) and satisfy the condition

a(t)a(t)=b(t)b(t),tR,a(t) a(-t)=b(t) b(-t),\quad t\in\mathbb{R},

we establish necessary and also sufficient conditions for the operators W(a)+H(b)W(a)+H(b) to be one-sided invertible, invertible or generalized invertible. Besides, efficient representations for the corresponding inverses are given.

Cite this article

Victor D. Didenko, Bernd Silbermann, Invertibility issues for a class of Wiener–Hopf plus Hankel operators. J. Spectr. Theory 11 (2021), no. 2, pp. 847–872

DOI 10.4171/JST/359