On inversion of semigroups of operators

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Home Editorial board Publication ethics Peer review guidelines Latest issue All issues Rules for authors Online submission system's guidelines Submit manuscript Contacts Address: Vatutina st. 53, Vladikavkaz, 362025, RNO-A, Russia Phone: (8672)23-00-54 E-mail: rio@smath.ru	DOI: 10.23671/VNC.2016.2.7391 On inversion of semigroups of operators Chshiev A. G. Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 2. Abstract: We study semigroups of linear relations in Banach space obtained by inversion of semigroups of bounded linear operators of different classes. As a basic research tool we use the orbit of a point. Also we use the common definition of the generator of a semigroup of linear relations. Keywords: semigroup of linear relation, semigroup of operators, generator of the semigroup, linear relation Language: Russian Download the full text For citation: Chshiev A. G. On inversion of semigroups of operators. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 2, pp.79-89. DOI 10.23671/VNC.2016.2.7391 + References 1. Baskakov A. G. Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations. Izvestiya: Mathematics, 2009, vol. 73, no. 2, pp. 215-278. 2. Hughes Rhonda Jo. Semigroups of unbounded linear operators in Banach space. Trans. Amer. Math. Soc., 1977, vol. 230, pp. 113-145. 3. Melnikova I. V. General Theory of Ill-Posed Cauchy Problem, 1995. 4. Lattes R., Lions Zh. L. Metod Kvaziobrashhenija i ego Prilozhenija, Moskva, Mir, 1970, 336 p. (Russian). 5. Ivanov V. K., Mel'nikova I. V., Filinkov A. I. Differencial'no-Operatornye Uravnenija i Nekorrektnye Zadachi, Moskva, Nauka, 1995, 176 p. (Russian). 6. Anufrieva U. A., Mel'nikova I. V. Peculiarities and regularization of ill-posed Cauchy problems with differential operators. J. Math. Sci., 2008, vol. 148, no. 4, pp. 481-632. 7. Cross R. Multivalued Linear Operators, New York, M. Dekker, 1998, 352 p. (Monogr. and Textbooks in Pure and Appl. Math. Vol. 213). 8. Favini A., Yagi A. Degenerate Differential Equations in Banach Spaces, N.Y., M. Dekker, 1998. 9. Hille Je. Funkcional'nyj Analiz I Polugruppy [Functional Analysis and Semi-Groups], Moskva, Izd-vo Inostr. Lit-ry, 1962, 829 p. (Russian). 10. Baskakov A. G. Linear relations as generators of semigroups of operators. Math. Notes, 2008, vol. 84, no. 1, pp. 166-183. 11. Baskakov A. G., Chernyshov K. I. Linear Relations, Differential Inclusions, and Degenerate Semigroups. Functional Analysis and Its Applications, 2002, vol. 36, no. 4, pp. 306-310. 12. Baskakov A. G., Chernyshov K. I. Spectral analysis of linear relations and degenerate operator semigroups. Sbornik: Mathematics, 2002, vol. 193, no. 11, pp. 1573-1610. 13. Chshiev A. G. The Gearhart-Prüss theorem for a class of degenerate semigroups of operators. Math. Notes, 2013, vol. 94, no. 3, pp. 400-413. 14. Baskakov A. G. Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations. Russian Math. Surveys, 2013, vol. 68, no. 1, pp. 69-116. 15. Chshiev A. G. The closeness and closability criteria for infinitesimal operators of certain semigroups. Russian Mathematics, 2011, vol. 55, no. 8, pp. 66-74. 16. Chshiev A. G. About Silchenko operators semigroup. Vladikavk. Mat. Zh. [Vladikavk. Math. J.], 2013, vol. 15, no. 4, pp. 82-90 (Russian). 17. Arens R. Operational calcules of linear relations. Pacific J. Math., 1961, vol. 11, pp. 9-23. 18. Zagorskij A. S. O polugruppah linejnyh otnoshenij. Vestn. VGU. Ser. Fiz.-Mat. [Proc. Voronezh State Univ. Ser. Phys. Math.], 2004, no. 2, pp. 158-161 (Russian). 19. Engel K. J., Nagel R. One-Parameter Semigroups for Linear Evolution Equations, New York, Springer Verlag, 2000, 586 p. The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses. ← Contents of issue


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