Geodesic
On the Fredholm Property of a Class of Convolution-Type Operators
Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 407-421

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The notions of the $\mathscr L$-convolution operator and the $\mathscr L$-Wiener–Hopf operator are introduced by replacing the Fourier transform in the definition of the convolution operator by a spectral transformation of the self-adjoint Sturm–Liouville operator on the axis $\mathscr L$. In the case of the zero potential, the introduced operators coincide with the convolution operator and the Wiener–Hopf integral operator, respectively. A connection between the $\mathscr L$-Wiener–Hopf operator and singular integral operators is revealed. In the case of a piecewise continuous symbol, a criterion for the Fredholm property and a formula for the index of the $\mathscr L$-Wiener–Hopf operator in terms of the symbol and the elements of the scattering matrix of the operator $\mathscr L$ are obtained.
Keywords: the operator $\mathscr L$-Wiener–Hopf, singular integral operator, Fredholm property. 
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     author = {A. G. Kamalian and I. M. Spitkovsky},
     title = {On the {Fredholm} {Property} of a {Class} of {Convolution-Type} {Operators}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {407--421},
     publisher = {mathdoc},
     volume = {104},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a6/}
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A. G. Kamalian; I. M. Spitkovsky. On the Fredholm Property of a Class of Convolution-Type Operators. Matematičeskie zametki, Tome 104 (2018) no. 3, pp. 407-421. http://geodesic.mathdoc.fr/item/MZM_2018_104_3_a6/