The spectrum of the Hausdorff operator on a subspace of L2(R)

Abstract

In this paper the space G2(R) is introduced and the boundedness, normality and spectral properties of the Hausdorff operator acting on the space G2(R) is investigated by using the theory of Fourier transform and Hilbert transform. Existence of spectrum of the Hausdorff operator on G2(R) is obtained. © 2013, by Oldenbourg Wissenschaftsverlag, München, Germany. All rights reserved.