Geodesic
Structural representation of inverse operator in Banach space
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2007), pp. 197-200.

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The problem of construction of inverse operator for the equation $Az=u$ ($u\in U$, $z\in F$; $U$, $F$ are metric spaces) is considered. The algorithm for solving the inverse problems based on structural representation of inverse operators as periodic structure is suggested. The necessary and sufficient conditions of fundamentality of periodic structure are formulated. It is shown that if these conditions are fulfilled the periodic structure operator converges to the inverse operator. 
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V. C. Tyan. Structural representation of inverse operator in Banach space. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2007), pp. 197-200. http://geodesic.mathdoc.fr/item/VSGTU_2007_1_a39/

[1] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1979 | MR

[2] A. N. Tikhonov, A. V. Goncharskii (red.), Nekorrektnye zadachi estestvoznaniya, MGU, M., 1987

[3] Tikhonov A. N., Kalner V. D., Glasko V. B., Matematicheskoe modelirovanie tekhnologicheskikh protsessov i metod obratnykh zadach v mashinostroenii, Mashinostroenie, M., 1990 | MR

[4] K. A. Pupkov, N. D. Egupov (red.), Metody klassicheskoi i sovremennoi teorii avtomaticheskogo upravleniya T. 2. Statisticheskaya dinamika i identifikatsiya sistem avtomaticheskogo upravleniya, MGTU, M., 2004

[5] Solodovnikov V. V., Semenov V. V., Spektralnaya teoriya nestatsionarnykh sistem upravleniya, Nauka, M., 1974

[6] Tikhonov A. N., Goncharovskii A. V., Stepanov V. V., Yagola A. G., Chislennye metody resheniya nekorrektnykh zadach, Nauka, M., 1990 | MR

[7] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1981 | MR

[8] Rapoport E. Ya., Tyan V. K., Dostizhenie zadannoi invariantnosti v stokhasticheskikh sistemakh kombinirovannogo upravleniya, Kuib. polit. in-t. Dep. v VINITI 20.06.89, No 4089-V89

[9] Tyan V. K., “Reshenie integralnogo uravneniya pervogo roda tipa svertki v nekorrektnykh zadachakh teorii upravleniya”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Tekhn. nauki, 2006, no. 40, 50–56

[10] Tyan V. K., “Teoriya periodicheskikh struktur v nekorrektnykh zadachakh sinteza invariantnykh i avtonomnykh sistem upravleniya”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Tekhn. nauki, 2006, no. 41, 47–54

[11] Tyan V. K., “Strukturnoe predstavlenie resheniya sistemy lineinykh algebraicheskikh uravnenii”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Fiz.-mat. nauki, 43 (2006), 158–162 | DOI