Geodesic
A problem on a~jump on a~contour with limit continuum
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 70-75.

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

We obtain a condition of resolvablity of boundary-value problem on restoring holomorphic function by a given jump on a contour with limit continuum. An example of such contour is a graph of the function $y=\sin\frac\pi x$, $0$, whose limit continuum is a segment $[-i,i]$ of imaginary axis.
Keywords: contour with limit continuum, analytic function, the jump boundary value problem. 
@article{IVM_2015_2_a7,
     author = {B. A. Kats and S. R. Mironova and A. Yu. Pogodina},
     title = {A problem on a~jump on a~contour with limit continuum},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {70--75},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_2_a7/}
}
TY  - JOUR
AU  - B. A. Kats
AU  - S. R. Mironova
AU  - A. Yu. Pogodina
TI  - A problem on a~jump on a~contour with limit continuum
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2015
SP  - 70
EP  - 75
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2015_2_a7/
LA  - ru
ID  - IVM_2015_2_a7
ER  - 
%0 Journal Article
%A B. A. Kats
%A S. R. Mironova
%A A. Yu. Pogodina
%T A problem on a~jump on a~contour with limit continuum
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2015
%P 70-75
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2015_2_a7/
%G ru
%F IVM_2015_2_a7
B. A. Kats; S. R. Mironova; A. Yu. Pogodina. A problem on a~jump on a~contour with limit continuum. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2015), pp. 70-75. http://geodesic.mathdoc.fr/item/IVM_2015_2_a7/

[1] Gakhov F. D., Kraevye zadachi, Nauka, M., 1977 | MR | Zbl

[2] Muskhelishvili N. I., Singulyarnye integralnye uravneniya, Nauka, M., 1962 | MR

[3] Jian-Ke Lu, Boundary value problems for analytic functions, World Scientific, Singapore, 1993 | MR | Zbl

[4] Kats B. A., “Kraevaya zadacha Rimana na negladkikh dugakh i fraktalnye razmernosti”, Algebra i analiz, 6:1 (1994), 172–202 | MR | Zbl

[5] Kats B. A., “The Riemann boundary value problem on non-rectifiable curves and related questions”, Complex Var. Elliptic Equ., 59:8 (2014), 1053–1069 | DOI | MR | Zbl

[6] Kats B. A., “Kraevaya zadacha Rimana na nespryamlyaemoi zhordanovoi krivoi”, DAN SSSR, 267:4 (1982), 789–792 | MR | Zbl

[7] Kats B. A., “Zadacha Rimana na zamknutoi zhordanovoi krivoi”, Izv. vuzov. Matem., 1983, no. 4, 68–80 | MR | Zbl

[8] Kats B. A., Mironova S. R., Pogodina A. Yu., “Ob odnom uslovii razreshimosti zadachi o skachke i ee prilozheniyakh”, Vestn. KGTU im. A. N. Tupoleva, 2011, no. 4, 110–118

[9] Kats B. A., Mironova S. R., Pogodina A. Yu., “Kraevaya zadacha Rimana–Gilberta dlya matrits na neglakoi duge”, Izvestiya NAN Armenii. Matematika, 47:4 (2012), 15–22 | MR

[10] Stein I., Singulyarnye integraly i differentsialnye svoistva funktsii, Mir, M., 1973 | MR | Zbl

[11] Vekua I. N., Obobschennye analiticheskie funktsii, Nauka, M., 1988 | MR | Zbl