Geodesic
Regularization of a class of summary equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 25-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $ D $ be an arbitrary quadrangle with boundary $\Gamma $. A four-element linear summation equation is considered. The solution is sought in the class of functions that are holomorphic outside $ D $ and disappear at infinity. The boundary values satisfy the Hölder condition on any compact set that does not contain vertices. At the vertices, at most, logarithmic singularities are allowed. Equation coefficients are functions holomorphic in $ D $. Their boundary values satisfy the Hölder condition on $ \Gamma $. The free term satisfies the same conditions. The solution is sought in the form of a Cauchy-type integral over $ \Gamma $ with unknown density. The Carleman problem is used to regularize the resulting functional equation. Previously, a Carleman shift is introduced on $\Gamma $, transferring each side to itself with a change in orientation. The midpoints of the sides are fixed shear points. Applications of this summary equation to the problem of moments for entire functions of exponential type are indicated.
Keywords: summary equation, equivalent regularization.
Mots-clés : Carleman problem 
@article{IVM_2021_9_a2,
     author = {F. N. Garif'yanov and E. V. Strezhneva},
     title = {Regularization of a class of summary equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--30},
     year = {2021},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_9_a2/}
}
TY  - JOUR
AU  - F. N. Garif'yanov
AU  - E. V. Strezhneva
TI  - Regularization of a class of summary equations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 25
EP  - 30
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_9_a2/
LA  - ru
ID  - IVM_2021_9_a2
ER  - 
%0 Journal Article
%A F. N. Garif'yanov
%A E. V. Strezhneva
%T Regularization of a class of summary equations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 25-30
%N 9
%U http://geodesic.mathdoc.fr/item/IVM_2021_9_a2/
%G ru
%F IVM_2021_9_a2
F. N. Garif'yanov; E. V. Strezhneva. Regularization of a class of summary equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2021), pp. 25-30. http://geodesic.mathdoc.fr/item/IVM_2021_9_a2/

[1] Garifyanov F. N., “O regulyarizatsii odnogo klassa raznostnykh uravnenii”, Sib. matem. zhurnal, 42:5 (2001), 1012–1017 | Zbl

[2] Garifyanov F. N., Modina S. A., “O chetyrekhelementnom uravnenii dlya funktsii, analiticheskikh vne trapetsii, i ego prilozheniyakh”, Sib. matem. zhurnal, 52:2 (2011), 243–249 | Zbl

[3] Garifyanov F. N., “Summarnoe uravnenie dlya funktsii, analiticheskikh vne chetyrekhugolnika”, Izv. vuzov. Matem., 2016, no. 10, 3–7 | Zbl

[4] Garifyanov F. N., “O summarnom uravnenii, porozhdennom chetyrekhugolnikom”, Izv. vuzov. Matem., 2018, no. 1, 27–33 | Zbl

[5] Garifyanov F. N., Strezhneva E. V., “O prilozheniyakh summarnogo uravneniya, indutsirovannogo chetyrekhugolnikom”, Ufimsk. matem. zhurn., 11:4 (2019), 29–34 | Zbl

[6] Zverovich E. I., “Metod lokalno-konformnogo skleivaniya”, Dokl. AN SSSR, 205:4 (1972), 767–770 | Zbl

[7] Aksenteva E. P., Garifyanov F. N., “K issledovaniyu integralnogo uravneniya s yadrom Karlemana”, Izv. vuzov. Matem., 1983, no. 4, 43–51 | Zbl

[8] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1967