Geodesic
The inverse of some class of operators in Banach space and its several applications
Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 55-60 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper deals with the method proposed for the inverse of some class of operators. The result is applied to some equations with closed operators. The examples are considered.
Keywords: Markov function, Krein class, functional calculus, closed operator, operator equation. 
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A. A. Atvinovskii; A. R. Mirotin. The inverse of some class of operators in Banach space and its several applications. Problemy fiziki, matematiki i tehniki, no. 3 (2013), pp. 55-60. http://geodesic.mathdoc.fr/item/PFMT_2013_3_a8/

[1] M. G. Krein, A. A. Nudelman, Problema momentov Markova i ekstremalnye zadachi, Nauka, M., 1973, 552 pp. | MR

[2] A. A. Atvinovskii, A. R. Mirotin, “Ob odnoznachnoi razreshimosti odnogo klassa operatornykh uravnenii”, Analiticheskie metody analiza i differentsialnykh uravnenii, Trudy 5-i mezhdunarodnoi konferentsii, v dvukh tomakh, v. 1, Matematicheskii analiz, In-t matem. NAN Belarusi, Minsk, 2012, 28–32

[3] A. A. Atvinovskii, “Ob integralnom predstavlenii odnogo klassa analiticheskikh funktsii”, Izv. Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 2011, no. 4 (67), 3–7

[4] A. R. Mirotin, “Obraschenie operatorno-monotonnykh funktsii negativnykh operatorov v banakhovom prostranstve”, Trudy instituta matematiki, 12:1 (2004), 104–108

[5] M. Haase, The functional calculus for sectorial operators, Birkhauser Verlag, Basel, 2006, 392 pp. | MR | Zbl

[6] Yu. A. Brychkov, A. P. Prudnikov, Integralnye preobrazovaniya obobschennykh funktsii, Nauka, M., 1977, 286 pp. | MR | Zbl

[7] D. V. Widder, The Laplace transform, Princeton, 1946, 406 pp. | MR

[8] M. A. Evgrafov, Analiticheskie funktsii, Nauka, M., 1991, 447 pp. | MR