Projection method for a class of integral operators with bihomogeneous kernels
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 3-11.

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

We consider the multidimensional integral operators with bihomogeneous kernels in the $L_2$–space. For such operators, the necessary and sufficient conditions for invertibility is obtained. The main result of the article is the applicability criterion of the projection method to a given class of operators with biohomogeneous kernels.
Keywords: integral operator, homogeneous kernel, invertibility, projection method, $C^*$-algebra.
@article{IVM_2023_3_a0,
     author = {O. G. Avsyankin},
     title = {Projection method for a class of integral operators with bihomogeneous kernels},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--11},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_3_a0/}
}
TY  - JOUR
AU  - O. G. Avsyankin
TI  - Projection method for a class of integral operators with bihomogeneous kernels
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 3
EP  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_3_a0/
LA  - ru
ID  - IVM_2023_3_a0
ER  - 
%0 Journal Article
%A O. G. Avsyankin
%T Projection method for a class of integral operators with bihomogeneous kernels
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 3-11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_3_a0/
%G ru
%F IVM_2023_3_a0
O. G. Avsyankin. Projection method for a class of integral operators with bihomogeneous kernels. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2023), pp. 3-11. http://geodesic.mathdoc.fr/item/IVM_2023_3_a0/

[1] Karapetiants N.K., Samko S.G., Equations with Involutive Operators, Birkhauser, Boston-Basel-Berlin, 2001 | MR | Zbl

[2] Avsyankin O.G., Karapetyants N.K., “Proektsionnyi metod v teorii integralnykh operatorov s odnorodnymi yadrami”, Matem. zametki, 75:2 (2004), 163–172 | DOI | Zbl

[3] Avsyankin O.G., Deundyak V.M., “Ob indekse mnogomernykh integralnykh operatorov s biodnorodnymi yadrami i peremennymi koeffitsientami”, Izv. vuzov. Matem., 2005, no. 3, 3–12 | Zbl

[4] Avsyankin O.G., “O $C^*$-algebre, porozhdennoi mnogomernymi integralnymi operatorami s odnorodnymi yadrami i operatorami multiplikativnogo sdviga”, Dokl. RAN, 419:6 (2008), 727–728 | MR | Zbl

[5] Avsyankin O.G., “Proektsionnyi metod dlya integralnykh operatorov s odnorodnymi yadrami, vozmuschennykh odnostoronnimi multiplikativnymi sdvigami”, Izv. vuzov. Matem., 2015, no. 2, 10–17 | Zbl

[6] Deundyak V.M., Lukin A.V., “Proektsionnyi metod resheniya uravnenii dlya mnogomernykh operatorov s anizotropno odnorodnymi yadrami kompaktnogo tipa”, Vestn. Udmurtsk. un-ta. Matem. Mekhan. Kompyut. nauki, 29:2 (2019), 153–165 | MR | Zbl

[7] Avsyankin O.G., “Ob obratimosti mnogomernykh integralnykh operatorov s biodnorodnymi yadrami”, Matem. zametki, 108:2 (2020), 291–295 | DOI | MR

[8] Avsyankin O.G., “Ob integralnykh operatorakh s odnorodnymi yadrami i trigonometricheskimi koeffitsientami”, Izv. vuzov. Matem., 2021, no. 4, 3–10

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

[10] Kozak A.V., “Lokalnyi printsip v teorii proektsionnykh metodov”, Dokl. AN SSSR, 212:6 (1973), 1287–1289 | Zbl

[11] Böttcher A., Silbermann B., Analysis of Toeplitz Operators, Springer-Verlag, Berlin-Heidelberg-New York, 1990 | MR | Zbl