Geodesic
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 L2–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.
Mots-clés : 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 = {https://geodesic-test.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  - https://geodesic-test.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 https://geodesic-test.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. https://geodesic-test.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