Geodesic
On $\mathbb R$-linear problem and truncated Wiener–Hopf equation
Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 21-33 
A. F. Voronin. On $\mathbb R$-linear problem and truncated Wiener–Hopf equation. Matematičeskie trudy, Tome 22 (2019) no. 2, pp. 21-33. http://geodesic.mathdoc.fr/item/MT_2019_22_2_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the $\mathbb R$-linear problem (also known as the Markushevich problem and the generalized Riemann boundary value problem) and the convolution integral equation of the second kind on a finite interval (also known as the truncated Wiener–Hopf equation). We find new conditions for correct solvability of the $\mathbb R$-linear problem and the truncated Wiener–Hopf equation.

[1] Boyarskii B. V., “Ob obobschennoi granichnoi zadache Gilberta”, Soobscheniya AN Gruz. SSR, 25:4 (1960), 385–390

[2] Voronin A. F., “Neobkhodimye i dostatochnye usloviya korrektnosti dlya uravneniya vtorogo roda v svertkakh na konechnom intervale s chetnym yadrom”, Sib. matem. zhurn., 49:4 (2008), 756–767 | MR | Zbl

[3] Voronin A. F., “Issledovanie integralnogo uravneniya vtorogo roda v svertkakh na konechnom intervale s periodicheskim yadrom”, Sib. zhurn. industr. matem., 12:1 (2009), 31–39 | Zbl

[4] Voronin A. F., “Sistemy uravnenii v svertkakh 1-go i 2-go roda na konechnom intervale i faktorizatsiya matrits-funktsii”, Sib. matem. zhurn., 53:5 (2012), 978–990 | MR | Zbl

[5] Voronin A. F., “Usloviya ustoichivosti i edinstvennosti resheniya zadachi Markushevicha”, Sib. elektron. matem. izv., 14 (2017), 511–517 | MR | Zbl

[6] Voronin A. F., “O svyazi obobschennoi kraevoi zadachi Rimana i usechennogo uravneniya Vinera–Khopfa”, Sib. elektron. matem. izv., 15 (2018), 412–421 | Zbl

[7] Voronin A. F., “Obobschennaya kraevaya zadacha Rimana i integralnye uravneniya v svertkakh pervogo i vtorogo roda na konechnom intervale”, Sib. elektron. matem. izv., 15 (2018), 1651–1662 | Zbl

[8] Gokhberg I. Ts., Krein M. G., “Sistemy integralnykh uravnenii na polupryamoi s yadrami, zavisyaschimi ot raznosti argumentov”, UMN, 13:2(80) (1958), 3–72

[9] Gokhberg I. Ts., Feldman I. A., Uravneniya v svertkakh i proektsionnye metody ikh resheniya, Nauka, M., 1971

[10] Litvinchuk G. S., “Dve teoremy ob ustoichivosti chastnykh indeksov kraevoi zadachi Rimana i ikh prilozhenie”, Izv. vuzov. Matem., 1967, no. 12, 47–57 | Zbl

[11] Mityushev V. V., “$\mathbb{R}$-Linear and Riemann–Hilbert problems for multiply connected domains”, Advances in Appl. Analysis, Trends Math., Birkhäuser, Basel, 2012, 147–176 | MR | Zbl