Inversion of a linear combination of values of the resolvent of a closed operator
Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 77-79.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of the computation of the left inverse of a linear combination of values of the resolvent of a closed operator in a Banach space is solved. Several unsolved problems are formulated.
Keywords: closed operator, left inverse of an operator, resolvent, Banach space, functional calculus, Markov function.
@article{PFMT_2014_3_a13,
     author = {A. R. Mirotin and A. A. Atvinovskii},
     title = {Inversion of a linear combination of values of the resolvent of a closed operator},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {77--79},
     publisher = {mathdoc},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2014_3_a13/}
}
TY  - JOUR
AU  - A. R. Mirotin
AU  - A. A. Atvinovskii
TI  - Inversion of a linear combination of values of the resolvent of a closed operator
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2014
SP  - 77
EP  - 79
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2014_3_a13/
LA  - ru
ID  - PFMT_2014_3_a13
ER  - 
%0 Journal Article
%A A. R. Mirotin
%A A. A. Atvinovskii
%T Inversion of a linear combination of values of the resolvent of a closed operator
%J Problemy fiziki, matematiki i tehniki
%D 2014
%P 77-79
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2014_3_a13/
%G ru
%F PFMT_2014_3_a13
A. R. Mirotin; A. A. Atvinovskii. Inversion of a linear combination of values of the resolvent of a closed operator. Problemy fiziki, matematiki i tehniki, no. 3 (2014), pp. 77-79. http://geodesic.mathdoc.fr/item/PFMT_2014_3_a13/

[1] N. Danford, Dzh. T. Shvarts, Lineinye operatory, v. 1, Obschaya teoriya, IL, M., 1962, 895 pp.

[2] A. A. Atvinovskii, A. R. Mirotin, “Ob odnom funktsionalnom ischislenii zamknutykh operatorov v banakhovom prostranstve”, Izvestiya vuzov. Matematika, 2013, no. 10, 3–15

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

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

[5] A. A. Atvinovskii, A. R. Mirotin, “Obraschenie odnogo klassa operatorov v banakhovom prostranstve i nekotorye ego primeneniya”, Problemy fiziki, matematiki i tekhniki, 2013, no. 3(16), 55–60

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

[7] V. S. Vladimirov, Obobschennye funktsii v matematicheskoi fizike, Nauka, M., 1979, 280 pp. | MR

[8] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972, 740 pp. | MR | Zbl