Geodesic
An integral equation with matrix difference kernel on an interval
Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1171-1177 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An equation of convolution type on an interval is considered. A realization of an extension of the corresponding integral operator in the form of an operator of Wiener-Hopf type is obtained. A result on the structure of the eigenspaces of the original operator and a criterion for its invertibility are proved on this basis. A formula enabling one to find the resolvent of the original operator given a factorization of the symbol of the auxiliary Wiener-Hopf operator is obtained. 
@article{SM_1998_189_8_a3,
     author = {V. M. Kaplitskii},
     title = {An integral equation with matrix difference kernel on an~interval},
     journal = {Sbornik. Mathematics},
     pages = {1171--1177},
     year = {1998},
     volume = {189},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_8_a3/}
}
TY  - JOUR
AU  - V. M. Kaplitskii
TI  - An integral equation with matrix difference kernel on an interval
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 1171
EP  - 1177
VL  - 189
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_8_a3/
LA  - en
ID  - SM_1998_189_8_a3
ER  - 
%0 Journal Article
%A V. M. Kaplitskii
%T An integral equation with matrix difference kernel on an interval
%J Sbornik. Mathematics
%D 1998
%P 1171-1177
%V 189
%N 8
%U http://geodesic.mathdoc.fr/item/SM_1998_189_8_a3/
%G en
%F SM_1998_189_8_a3
V. M. Kaplitskii. An integral equation with matrix difference kernel on an interval. Sbornik. Mathematics, Tome 189 (1998) no. 8, pp. 1171-1177. http://geodesic.mathdoc.fr/item/SM_1998_189_8_a3/

[1] Gokhberg I. Ts., Krein M. G., “Sistemy integralnykh uravnenii na polupryamoi s yadrom, zavisyaschim ot raznosti argumentov”, UMN, 13:2 (1958), 3–72 | MR

[2] Gokhberg I. Ts., “Zadacha faktorizatsii v normirovannykh koltsakh, funktsii ot izometricheskikh i simmetricheskikh operatorov i singulyarnye integralnye uravneniya”, UMN, 19:1 (1964), 71–124 | MR | Zbl

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

[4] Ganin M. R., “Ob integralnom uravnenii Fredgolma s yadrom, zavisyaschim ot raznosti argumentov”, Izv. vuzov. Ser. matem., 1973, no. 2 (129), 31–43 | MR

[5] Paltsev B. V., “Razlozheniya po sobstvennym funktsiyam integralnykh operatorov svertki na konechnom intervale s yadrami, preobrazovaniya Fure kotorykh ratsionalny. “Slabo” nesamosopryazhennye regulyarnye yadra”, Izv. AN SSSR. Ser. matem., 36:3 (1972), 591–634 | MR | Zbl

[6] Paltsev B. V., “Asimptotika spektra i sobstvennykh funktsii operatorov svertki s odnorodnym preobrazovaniem Fure yadra”, Dokl. AN SSSR, 218:1 (1974), 28–31 | MR | Zbl

[7] Paltsev B. V., “Uravnenie svertki na konechnom intervale dlya odnogo klassa simvolov, imeyuschikh stepennuyu asimptotiku na beskonechnosti”, Izv. AN SSSR. Ser. matem., 44:2 (1980), 322–394 | MR | Zbl

[8] Karlovich Yu. F., Spitkovskii I. M., “O neterovosti nekotorykh singulyarnykh integralnykh operatorov s matrichnymi koeffitsientami klassa SAP i svyazannykh s nimi sistemakh uravnenii svertki na konechnom promezhutke”, Dokl. AN SSSR, 269:3 (1983), 531–535 | MR | Zbl

[9] Komyak I. I., “O reshenii v kvadraturakh integralnogo uravneniya Fredgolma s yadrom, zavisyaschim ot raznosti argumentov”, Izv. AN BSSR. Ser. fiz.-matem. nauk, 20:2 (1973), 45–52

[10] Krein M. G., “Ob opredelenii potentsiala chastitsy po ee $S$-funktsii”, Dokl. AN SSSR, 105:3 (1955), 433–436 | MR | Zbl

[11] Tsvelik A. M., “Tochnoe reshenie modeli odnomernykh fermionov s simmetriei $SU(N)\otimes SU(M)$”, ZhETF, 93:4 (1987), 1329–1340 | MR

[12] Sakhnovich L. A., “Uravnenie s raznostnym yadrom na konechnom otrezke”, UMN, 35:4 (1980), 69–129 | MR | Zbl

[13] Baxter G., Hirschman I. I., Jr., “An explicit inversion formula for finite-section Wiener–Hopf operators”, Bill. Amer. Math. Soc., 70 (1964), 820–823 | DOI | MR | Zbl

[14] Hirschman I. I., Jr., “Finite section Wiener–Hopf equations on a compact group with ordered dual”, Bull. Amer. Math. Soc., 70 (1964), 508–510 | DOI | MR | Zbl