On a Class of L-Wiener-Hopf Operators

Abstract

By replacement in the definition of the convolution operator of Fourier transform by a spectral transform of a selfadjoint Sturm-Liouville operator on the axis L, the concepts of Lconvolution and L-Wiener-Hopf operators are introduced. The case of the reflectorless potentials with a single eigenvalue is considered. A relationship between the Wiener-Hopf and L-Wiener- Hopf operators is established. In the case of piecewise continuous symbol the Fredholm property and invertibility of the L-Wiener-Hopf operator are investigated.