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

On correct linear differential operators

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.

DOI: https://doi.org/10.4213/sm390

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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

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
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\pages 323--348
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• http://mi.mathnet.ru/eng/msb390
• https://doi.org/10.4213/sm390
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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. A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698
2. Tyurin V.M., “On the Fredholm property of linear operators of elliptic type on $R^n$”, Differ. Equ., 40:2 (2004), 265–270
3. Latushkin Yu., Tomilov Yu., “Fredholm properties of evolution semigroups”, Illinois J. Math., 48:3 (2004), 999–1020
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
5. Latushkin, Y, “Fredholm differential operators with unbounded coefficients”, Journal of Differential Equations, 208:2 (2005), 388
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
7. Latushkin, Y, “Dichotomy and Fredholm properties of evolution equations”, Journal of Operator Theory, 58:2 (2007), 387
8. Baskakov, AG, “On differential and difference Fredholm operators”, Doklady Mathematics, 76:2 (2007), 669
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
10. Latushkin, Y, “The Dichotomy Theorem for evolution bi-families”, Journal of Differential Equations, 245:8 (2008), 2267
11. Aldroubi, A, “Slanted matrices, Banach frames, and sampling”, Journal of Functional Analysis, 255:7 (2008), 1667
12. M. S. Bichegkuev, “Linear Difference and Differential Operators with Unbounded Operator Coefficients in Weight Spaces”, Math. Notes, 86:5 (2009), 637–644
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
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
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
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
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
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
19. A. G. Baskakov, V. B. Didenko, “Spectral analysis of differential operators with unbounded periodic coefficients”, Diff Equat, 51:3 (2015), 325
20. Bichegkuev M.S., “Spectral Analysis of Differential Operators With Unbounded Operator Coefficients on the Half-Line”, Differ. Equ., 51:4 (2015), 431–439
21. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232
22. M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36
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
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
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