Geodesic
On functional equations related to a~dihedral group
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 33-41.

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

We propose a method for regularization of two three-element functional equations generated by a special case of dihedral group of rotations. These results are applied to the moment problem for entire functions of exponential type and for evaluation of biorthogonally dual systems of analytic functions.
Keywords: regularization, Carleman boundary-value problem, problem on moments. 
@article{IVM_2014_11_a3,
     author = {F. N. Garifyanov and A. F. Garifyanov},
     title = {On functional equations related to a~dihedral group},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {33--41},
     publisher = {mathdoc},
     number = {11},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_11_a3/}
}
TY  - JOUR
AU  - F. N. Garifyanov
AU  - A. F. Garifyanov
TI  - On functional equations related to a~dihedral group
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 33
EP  - 41
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_11_a3/
LA  - ru
ID  - IVM_2014_11_a3
ER  - 
%0 Journal Article
%A F. N. Garifyanov
%A A. F. Garifyanov
%T On functional equations related to a~dihedral group
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 33-41
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_11_a3/
%G ru
%F IVM_2014_11_a3
F. N. Garifyanov; A. F. Garifyanov. On functional equations related to a~dihedral group. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2014), pp. 33-41. http://geodesic.mathdoc.fr/item/IVM_2014_11_a3/

[1] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, GITTL, M.–L., 1950

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

[3] Garifyanov F. N., “Biortogonalnye ryady porozhdennye gruppoi diedra”, Izv. vuzov. Matem., 2001, no. 4, 11–15 | MR | Zbl

[4] Carleman T., “Sur la théorie des équations intégrales et ses applications”, Verh. Int. Math. Kongresses, v. I, Zurich, 1932, 138–151 | Zbl

[5] Garifyanov F. N., Modina S. A., “Yadro Karlemana i ego prilozheniya”, Sib. matem. zhurn., 53:6 (2012), 1263–1273 | MR | Zbl

[6] Garifyanov F. N., “Problema obrascheniya osobogo integrala i raznostnye uravneniya dlya funktsii, analiticheskikh vne kvadrata”, Izv. vuzov. Matem., 1993, no. 7, 7–16 | MR | Zbl

[7] Aksenteva E. P., Garifyanov F. N., “O lakunarnykh analogakh teta-ryada Puankare i ikh prilozhenii”, Sib. matem. zhurn., 43:5 (2002), 977–986 | MR | Zbl

[8] Biberbakh L., Analiticheskoe prodolzhenie, Nauka, M., 1976

[9] Khavin V. P., “Prostranstva analiticheskikh funktsii”, Itogi nauki i tekhniki. Matem. analiz 1964, VINITI, M., 1966, 76–164 | MR

[10] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956

[11] Leontev A. F., Ryady eksponent, Nauka, M., 1976 | MR | Zbl