Geodesic
Discrete convolution operators with almost-stabilized coefficients
Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 339-344

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For a convolution operator of the form $K=\sum_j=0^{N-1}P_jA_j$, where $A_j$ are discrete Wiener—Hopf operators and $P_j$ are coordinate projections whose indices are congruent to $j$ modulo $N$, necessary and sufficient conditions for it to be Nötherian in $L_{p+}$ ($1\le p\le\infty$), $c_+^0$ and formulas for the index are obtained. 
@article{MZM_1977_22_3_a2,
     author = {N. K. Karapetyants and S. G. Samko},
     title = {Discrete convolution operators with almost-stabilized coefficients},
     journal = {Matemati\v{c}eskie zametki},
     pages = {339--344},
     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a2/}
}
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N. K. Karapetyants; S. G. Samko. Discrete convolution operators with almost-stabilized coefficients. Matematičeskie zametki, Tome 22 (1977) no. 3, pp. 339-344. http://geodesic.mathdoc.fr/item/MZM_1977_22_3_a2/