•  
  •  
 

Scientific Journal of Samarkand University

Abstract

We study new problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. We prove uniqueness theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev’s spaces and thus show their weak illposedness.

First Page

12

Last Page

18

References

1. Lavrentev M.M., Savelev L.YA. Teoriya operatorov i nekorrektnye zadachi. – Novosibirsk: Izd-vo In-ta matematiki. 1999. – 702 s. 2. Lavrentev A.M., Shabat B.V. Metody teorii funksiy kompleksnogo peremennogo.  M.: Nauka, 1986. 3. Romanov V. G. O vosstanovlenii funksii cherez integraly po ellipsoidam vrasheniya, u kotoryx fokus nepodvijen // Dokl. AN SSSR.  Moskva, 1967. T. 173.  № 4.  S. 766-769. 4. Romanov V. G. O vosstanovlenii funksii cherez integraly po semeystvu krivyx // Sib. mat. jurn., 1967. T. 8.  № 5.  S. 1206-1208. 5. Buxgeym A.L. O nekotoryx zadachax integralnoy geometrii // Sib. mat. jurn., 1972. T. 13.  № 1.  S. 34- 42. 6. Buxgeym A.L. Ob odnoy zadache integralnoy geometrii // Mat. problemy geofiziki.  Novosibirsk: VS SO AN SSSR, 1973. Vyp. 4.  S. 69-73. 7. Begmatov Akr a m X. Slabo nekorrektnye zadachi integralnoy geometrii volterrovskogo tipa // Doklady RAN.  Moskva, 1996. T. 349.  № 3.  S. 297-298. 8. Begmatov Akr a m X. Zadachi integralnoy geometrii dlya semeystva konusov v n-mernom prostranstve // Sib. mat. jurn., 1996. T. 37.  № 3.  S. 500-505. 9. Begmatov Akr a m X. Novye klassy slabo i silno nekorrektnyx zadach integralnoy geometrii // Vtoroy Sib. kongress po prikl. i ind. matematike. Tez. dokl., ch. III.  Novosibirsk: Institut matematiki SO RAN, 1996.  S. 298. 10. Begmatov Akr am X. Nekotorыe novыe klassы zadach integralnoy geometrii.  Novosibirsk, 1997. Preprint / RAN. Sibirskoe otdelenie. Institut matematiki.  № 40, 30 s. 11. Begmatov Akr a m X. Volterrovskie zadachi integralnoy geometrii na ploskosti dlya krivyx s osobennostyami // Sib. mat. jurn., 1997. T. 38.  № 4.  S. 723-737. 12. Begmatov Akram X. Zadachi integralnoy geometrii po spetsialnym krivym i poverxnostyam s osobennostyami v vershine // Doklady RAN.  Moskva, 1998. T. 358.  № 2.  S. 151-153. 13. Begmatov Akram X. Teoremy sushestvovaniya resheniya dvux slabo nekorrektnyx zadach integralnoy geometrii // Doklady RAN.  Moskva, 2002. T. 386.  № 1.  S. 1-3. 14. Begmatov Akram X., Ochilov Z.X. Zadachi integralnoy geometrii s razryvnoy vesovoy funksiey // Dokladы RAN.  Moskva, 2009. 429.  № 3.  C. 295-297. 15. Begmatov Akram H., Ochilov Z.H. Recovering of function set by integrals along a curve in the plane // Ill-Pozed and Non-Classical Problems of Mathematical Physics and Analysis, M.M. Lavrent’ev et al., Eds., Proceedings of International Converence, VSP.  UtrechtBoston, 2003.  S. 191-197. 16. Begmatov Akram X., Ochilov Z.X. Zadachi integralnoy geometrii volterovskogo tipa s vesovoy funksiey spetsialnogo vida. Jurnal Continuum: Matematika. Informatika. Obrazovanie. Rossiya 2017 g., № 2., S. 11-15.

Included in

Mathematics Commons

Share

COinS