Error message

  • Notice: Undefined index: und in citing_article_block_content() (line 310 of /www/izvestiya/sites/all/modules/custom/citing_an_article/citing_an_article.module).
  • Notice: Undefined index: und in citing_article_block_content() (line 313 of /www/izvestiya/sites/all/modules/custom/citing_an_article/citing_an_article.module).

Cite this article as:

Didenko V. B. About reversibility states of linear differential operators with periodic unbounded operator coefficients . Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2014, vol. 14, iss. 2, pp. 136-?.


Heading: 
UDC: 
517.937, 517.983

About reversibility states of linear differential operators with periodic unbounded operator coefficients

Abstract: 

For investigated linear differential operator (equation) with unbounded periodic operator coefficients defined at one of the Banach space of vector functions defined on all real axis difference operator (equation) with constant operator coefficient defined at appropriate Banach space of two-side vector sequences is considered. For differential and difference operators propositions about kernel and co-image dimensions coincidence, simultaneous complementarity of kernels and images, simultaneous reversibility, spectrum interrelation are proved.

References
1. Krein S. G. Linear Differential Equations in Banach Space. American Math. Soc., 1971. 390 p.
2. Howland J . S. Stationary scattering theory for timedependent Hamiltonians. Math. Ann., 1974, vol. 207, no. 4., pp. 315–335.
3. Baskakov A. G. Spectral analysis of linear differential operators and semi-groups of difference operators. Doklady Mathematics, 1995, vol. 343, no. 3, pp. 295–298 (in Russian).
4. Baskakov A. G. Semigroups of difference operators in spectral analysis of linear differential operators. Functional Analysis and Its Applications, 1996, vol. 30, no. 3, pp. 149–157. DOI: 10.1007/BF02509501.
5. Hille E., Phillips R. S. Functional Analysis and Semi-groups. American Math. Soc., 1957, 808 p.
6. Henry D. Geometric Theory of Semilinear Parabolic Equations. Springer, 1993. 350 p.
7. Baskakov A. G., Pastukhov A. I. Spectral Analysis of a Weighted Shift Operator with Unbounded Operator Coefficients. Siberian Math. J., 2001, vol. 42, no. 6, pp. 1026–1036. DOI: 10.1023/A:1012832208161.
8. Dunford N., Schwartz J. T. Linear Operators: General theory. Interscience Publishers, 1958. 2592 p.
9. Didenko V. B. On the spectral properties of differential operators with unbounded operator coefficients determined by a linear relation. Math. Notes, 2011, vol. 89, no. 2, pp. 224–237. DOI: 10.1134/S0001434611010287.
10. Didenko V. B. On the continuous invertibility and the Fredholm property of differential operators with multivalued impulse effects. Izvestiya : Mathematics, 2013, vol. 77, no. 1, pp. 3–19. DOI: 10.1070/IM2013v077n01ABEH002626.
11. Baskakov A. G., Kobychev K. S. Estimates for the embedding operator of a sobolev space of periodic functions and for the solutions of differential equations with periodic coefficients. Differential Equations, 2011, vol. 47, no. 5, pp. 609–619. DOI:10.1134/S0012266111050016.
12. Perov A. I. Frequency tests for the existence of boundary solutions. Differential Equations, 2007, vol. 43, no. 7, pp. 916–924. DOI: 10.1134/S001226610707004X.
13. Perov A. I. Frequency methods in the theory of bounded solutions of nonlinear nth-order differential equations (existence, almost periodicity, and stability). Differential Equations, 2012, vol. 48, no. 5, pp. 670–680. DOI:10.1134/S0012266112050059.
14. Baskakov A. G. On correct linear differential operators. Sbornik : Mathematics, 1999, vol. 190, no. 3, pp. 323–348. DOI: 10.1070/SM1999v190n03ABEH000390.
15. Baskakov A. G. Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations. Russian Math. Surv., 2013, vol. 68, no. 1, pp. 69–116. DOI: RM2013v068n01ABEH004822.
16. Baskakov A. G. Linear differential operators with unbounded operator coefficients and semigroups of bounded operators. Math. Notes, 1996, vol. 59, no. 6, pp. 586–593. DOI: 10.1007/BF02307207.
17. Baskakov A. G. Spectral analysis of differential operators and semi-groups of difference operators I. Differential Equations, 1996, vol. 33, no. 10, pp. 1299–1306 (in Russian).
18. Baskakov A. G. Spectral analysis of differential operators and semi-groups of difference operators II.
Differential Equations, 2001, vol. 37, no. 1, pp. 1–10.DOI: 10.1023/A:1019298028556.
19. Baskakov A. G., Sintyaev Yu. N. Finite-difference operators in the study of differential operators: Solution estimates. Differential Equations, 2010, vol. 46, no. 2, pp. 214–223. DOI: 10.1134/S0012266110020072.
Short text (in English): 
Full text: