Geodesic
On the invertibility conditions of finite-difference operators
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 94-101

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The invertibility of second-order finite-difference operators with constant operator coefficients acting in the Banach space of two-sided vector sequences is proved under the condition of their uniform injectivity (in particular, left invertibility) or surjectivity (in particular, right invertibility) or Fredholm property.
Keywords: second-order finite-difference operator, uniform injectivity, surjectivity, Fredholm property, spectrum, invertibility. 
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     author = {L. Yu. Kabantosva},
     title = {On the invertibility conditions of finite-difference operators},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {94--101},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a7/}
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L. Yu. Kabantosva. On the invertibility conditions of finite-difference operators. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 94-101. http://geodesic.mathdoc.fr/item/INTO_2019_171_a7/