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Mat. Zametki, 2000, Volume 67, Issue 6, Pages 816–827 (Mi mz900)  

This article is cited in 22 scientific papers (total in 22 papers)

Invertibility and the Fredholm property of difference operators

A. G. Baskakov

Voronezh State University

DOI: https://doi.org/10.4213/mzm900

Full text: PDF file (200 kB)
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English version:
Mathematical Notes, 2000, 67:6, 690–698

Bibliographic databases:

UDC: 517.9
Received: 07.04.1999

Citation: A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Mat. Zametki, 67:6 (2000), 816–827; Math. Notes, 67:6 (2000), 690–698

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. E. Slyusarchuk, “Necessary and sufficient conditions for the invertibility of the non-linear difference operator $(\mathscr Dx)(t)=x(t+1)-f(x(t))$ in the space of bounded continuous functions on the real axis”, Sb. Math., 192:4 (2001), 565–576  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Baskakov, AG, “On invertibility and the Fredholm property of parabolic differential operators”, Doklady Mathematics, 65:2 (2002), 245  mathscinet  zmath  isi
    3. Latushkin, Y, “Fredholm differential operators with unbounded coefficients”, Journal of Differential Equations, 208:2 (2005), 388  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    4. Baskakov, AG, “On differential and difference Fredholm operators”, Doklady Mathematics, 76:2 (2007), 669  mathnet  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    5. A. G. Baskakov, “Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations”, Izv. Math., 73:2 (2009), 215–278  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. V. E. Slyusarchuk, “Conditions for the invertibility of the nonlinear difference operator $(\mathscr Rx)(n)=H(x(n),x(n+1))$, $n\in\mathbb Z$, in the space of bounded number sequences”, Sb. Math., 200:2 (2009), 261–282  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. Poetzsche Ch., “Nonautonomous Bifurcation of Bounded Solutions I: a Lyapunov-Schmidt Approach”, Discrete Contin. Dyn. Syst.-Ser. B, 14:2, SI (2010), 739–776  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Poetzsche Ch., “Nonautonomous Bifurcation of Bounded Solutions II: a Shovel-Bifurcation Pattern”, Discret. Contin. Dyn. Syst., 31:3 (2011), 941–973  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Poetzsche Ch., “Persistence and Imperfection of Nonautonomous Bifurcation Patterns”, J. Differ. Equ., 250:10 (2011), 3874–3906  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    10. Poetzsche Ch., “Nonautonomous Continuation of Bounded Solutions”, Commun. Pure Appl. Anal, 10:3 (2011), 937–961  crossref  mathscinet  zmath  isi  scopus  scopus
    11. Pejsachowicz J., Skiba R., “Global Bifurcation of Homoclinic Trajectories of Discrete Dynamical Systems”, Cent. Eur. J. Math., 10:6 (2012), 2088–2109  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    12. Poetzsche Ch., “Fine Structure of the Dichotomy Spectrum”, Integr. Equ. Oper. Theory, 73:1 (2012), 107–151  crossref  mathscinet  zmath  isi  scopus  scopus
    13. Poetzsche Ch., “Corrigendum on: a Note on the Dichotomy Spectrum (Vol 15, Pg 1021, 2009)”, J. Differ. Equ. Appl., 18:7 (2012), 1257–1261  crossref  mathscinet  zmath  isi  scopus  scopus
    14. A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. M. S. Bichegkuev, “Spectral analysis of difference and differential operators in weighted spaces”, Sb. Math., 204:11 (2013), 1549–1564  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. Todorov D., “Generalizations of Analogs of Theorems of Maizel and Pliss and their Application in Shadowing Theory”, Discret. Contin. Dyn. Syst., 33:9 (2013), 4187–4205  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. A. Yu. Duplishcheva, “About Conditions of Invertibility of Difference Operators of the Second Order”, J. Math. Sci., 213:6 (2016), 832–837  mathnet  crossref
    18. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    19. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  isi  elib
    20. Baskakov A.G. Kabantsova L.Yu. Kostrub I.D. Smagina T.I., “Linear differential operators and operator matrices of the second order”, Differ. Equ., 53:1 (2017), 8–17  crossref  mathscinet  zmath  isi  scopus
    21. Poetzsche Ch., Skiba R., “Global Continuation of Homoclinic Solutions”, Z. Anal. ihre. Anwend., 37:2 (2018), 159–187  crossref  mathscinet  zmath  isi  scopus  scopus
    22. Boichuk O.A., Zhuravl'ov V.P., Pokutnyi O.O., “Bounded Solutions of Evolutionary Equations”, Ukr. Math. J., 70:1 (2018), 5–29  crossref  mathscinet  isi  scopus
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