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Mat. Sb., 1999, Volume 190, Number 3, Pages 3–28 (Mi msb390)  

This article is cited in 24 scientific papers (total in 24 papers)

On correct linear differential operators

A. G. Baskakov

Voronezh State University

Abstract: Given a family of evolution operators, a linear differential operator in the Banach space of vector-valued functions on the semiaxis is constructed. Results on its correctness (uniform injectivity) and left invertibility are obtained.


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English version:
Sbornik: Mathematics, 1999, 190:3, 323–348

Bibliographic databases:

UDC: 517.9
MSC: Primary 47B38, 47B39, 35K22; Secondary 47B37
Received: 21.01.1997 and 13.02.1998

Citation: A. G. Baskakov, “On correct linear differential operators”, Mat. Sb., 190:3 (1999), 3–28; Sb. Math., 190:3 (1999), 323–348

Citation in format AMSBIB
\by A.~G.~Baskakov
\paper On correct linear differential operators
\jour Mat. Sb.
\yr 1999
\vol 190
\issue 3
\pages 3--28
\jour Sb. Math.
\yr 1999
\vol 190
\issue 3
\pages 323--348

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    This publication is cited in the following articles:
    1. A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Tyurin V.M., “On the Fredholm property of linear operators of elliptic type on $R^n$”, Differ. Equ., 40:2 (2004), 265–270  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    3. Latushkin Yu., Tomilov Yu., “Fredholm properties of evolution semigroups”, Illinois J. Math., 48:3 (2004), 999–1020  mathscinet  zmath  isi
    4. Di Giorgio, D, “Optimal regularity and Fredholm properties of abstract parabolic operators in L-p spaces on the real line”, Proceedings of the London Mathematical Society, 91 (2005), 703  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Latushkin, Y, “Fredholm differential operators with unbounded coefficients”, Journal of Differential Equations, 208:2 (2005), 388  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    6. Sasu, B, “Exponential dichotomy and (l(p), l(q))-admissibility on the half-line”, Journal of Mathematical Analysis and Applications, 316:2 (2006), 397  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    7. Latushkin, Y, “Dichotomy and Fredholm properties of evolution equations”, Journal of Operator Theory, 58:2 (2007), 387  mathscinet  zmath  isi  scopus  scopus  scopus
    8. Baskakov, AG, “On differential and difference Fredholm operators”, Doklady Mathematics, 76:2 (2007), 669  mathnet  crossref  mathscinet  zmath  isi  elib
    9. Aldroubi A., Baskakov A., Krishtal I., “On slanted matrices in frame theory - art. no. 67010Q”, Wavelets XII, Proceedings of the Society of Photo-Optical Instrumentation Engineers (Spie), 6701, no. 1-2, 2007, Q7010–Q7010  isi
    10. Latushkin, Y, “The Dichotomy Theorem for evolution bi-families”, Journal of Differential Equations, 245:8 (2008), 2267  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. Aldroubi, A, “Slanted matrices, Banach frames, and sampling”, Journal of Functional Analysis, 255:7 (2008), 1667  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    12. M. S. Bichegkuev, “Linear Difference and Differential Operators with Unbounded Operator Coefficients in Weight Spaces”, Math. Notes, 86:5 (2009), 637–644  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    13. 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
    14. Kuznetsova T.B., Tyurin V.M., “On Linear Differential Phi(+)-Operators of Elliptic Type in Sobolev-Stepanov Spaces”, Differ Equ, 47:3 (2011), 443–445  crossref  mathscinet  zmath  isi  elib  elib
    15. 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
    16. M. S. Bichegkuev, “Spectral Analysis of Differential Operators with Unbounded Operator Coefficients in Weighted Spaces of Functions”, Math. Notes, 95:1 (2014), 15–21  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    17. V. B. Didenko, “O sostoyaniyakh obratimosti lineinykh differentsialnykh operatorov s neogranichennymi periodicheskimi koeffitsientami”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 14:2 (2014), 136–144  mathnet
    18. A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 1–10  mathnet  crossref
    19. A. G. Baskakov, V. B. Didenko, “Spectral analysis of differential operators with unbounded periodic coefficients”, Diff Equat, 51:3 (2015), 325  crossref  mathscinet  zmath
    20. Bichegkuev M.S., “Spectral Analysis of Differential Operators With Unbounded Operator Coefficients on the Half-Line”, Differ. Equ., 51:4 (2015), 431–439  crossref  mathscinet  zmath  isi  elib
    21. 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
    22. M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36  mathnet  crossref  crossref  mathscinet  isi  elib
    23. 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
    24. A. G. Baskakov, L. Yu. Kabantsova, T. I. Smagina, “Invertibility conditions for second-order differential operators in the space of continuous bounded functions”, Differ. Equ., 54:3 (2018), 285–294  crossref  crossref  mathscinet  zmath  isi  elib  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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