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 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{INTO_2019_171_a7,
     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},
     year = {2019},
     volume = {171},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a7/}
}
TY  - JOUR
AU  - L. Yu. Kabantosva
TI  - On the invertibility conditions of finite-difference operators
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 94
EP  - 101
VL  - 171
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_171_a7/
LA  - ru
ID  - INTO_2019_171_a7
ER  - 
%0 Journal Article
%A L. Yu. Kabantosva
%T On the invertibility conditions of finite-difference operators
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 94-101
%V 171
%U http://geodesic.mathdoc.fr/item/INTO_2019_171_a7/
%G ru
%F INTO_2019_171_a7
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/

[1] Baskakov A. G., “Spektralnyi analiz operatora vzveshennogo sdviga s neogranichennymi operatornymi koeffitsientami”, Sib. mat. zh., 42:6 (2001), 1231–1243 | MR | Zbl

[2] Baskakov A. G., “Spektralnyi analiz differentsialnykh operatorov s neogranichennymi operatornymi koeffitsientami, raznostnye otnosheniya i polugruppy raznostnykh otnoshenii”, Izv. RAN. Ser. mat., 7:2 (2009), 3–68 | DOI

[3] Baskakov A.G., “Raznostnye operatory i operatornye matritsy vtorogo poryadka”, Izv. RAN. Ser. mat., 79:2 (2015), 3–20 | DOI | MR | Zbl

[4] Danford N., Lineinye operatory. Obschaya teoriya, v. 1, IL, M., 1962

[5] Kolmogorov A. N., Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2004

[6] Aldloubi A., Baskakov A., Krishtal I., “Slanted matrices, Banach frames and sampling”, J. Funct. Anal., 255 (2008), 1667–1691 | DOI | MR

[7] Kurbatov V. G., Functional-Differential Operators and Equations, Kluwer Academic Publ., Dordrecht, 1999 | MR | Zbl