Asymptotic behavior of the spectrum of weakly polar integral
Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1151-1168.

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

The principal term is calculated for an asymptotic expression for the spectrum of multidimensional symmetric integral operators of potential type.
@article{IM2_1970_4_5_a8,
     author = {M. Sh. Birman and M. Z. Solomyak},
     title = {Asymptotic behavior of the spectrum of weakly polar integral},
     journal = {Izvestiya. Mathematics },
     pages = {1151--1168},
     publisher = {mathdoc},
     volume = {4},
     number = {5},
     year = {1970},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a8/}
}
TY  - JOUR
AU  - M. Sh. Birman
AU  - M. Z. Solomyak
TI  - Asymptotic behavior of the spectrum of weakly polar integral
JO  - Izvestiya. Mathematics 
PY  - 1970
SP  - 1151
EP  - 1168
VL  - 4
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a8/
LA  - en
ID  - IM2_1970_4_5_a8
ER  - 
%0 Journal Article
%A M. Sh. Birman
%A M. Z. Solomyak
%T Asymptotic behavior of the spectrum of weakly polar integral
%J Izvestiya. Mathematics 
%D 1970
%P 1151-1168
%V 4
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a8/
%G en
%F IM2_1970_4_5_a8
M. Sh. Birman; M. Z. Solomyak. Asymptotic behavior of the spectrum of weakly polar integral. Izvestiya. Mathematics , Tome 4 (1970) no. 5, pp. 1151-1168. http://geodesic.mathdoc.fr/item/IM2_1970_4_5_a8/

[1] Birman M. Sh., Solomyak M. Z., “O glavnom chlene spektralnoi asimptotiki negladkikh ellipticheskikh zadach”, Funkts. analiz, 4:4 (1970), 1–14 | MR

[2] Weyl H., “Die asymptoitiisihe Verteilungsgesetze der Eigenwerte partieller Differentialglaichungen”, Math. Ann., 71 (1912), 441–479 | DOI | MR | Zbl

[3] Gokhberg I. Ts., Krein M. G., Vvedenie v teoriyu lineinykh nesamosopryazhennykh operatorov, Nauka, M., 1965

[4] Birman M. Sh., Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov. I”, Vestn. LGU, 1967, no. 7, 43–53 | MR | Zbl

[5] Birman M. Sh., Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov. II”, Vestn. LGU, 1967, no. 13, 21–28 | MR | Zbl

[6] Birman M. Sh., Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov. III”, Vestn. LGU, 1969, no. 1, 35–48 | MR | Zbl

[7] Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov. IV”, Vestn. LGU, 1970, no. 1, 76–87 | Zbl

[8] Kostometov G. P., Solomyak M. Z., “Ob otsenkakh singulyarnykh chisel integralnykh operatorov, yadra kotorykh imeyut osobennost na diagonali”, v pechati, Vestnik LGU

[9] Mordasova G. M., “Asimptotika sobstvennykh znachenii lineinogo integralnogo uravneniya s razryvnym yadrom”, Dokl. AN SSSR, 142 (1962), 1022–1025 | MR | Zbl

[10] Zakhar-Itkin M. X., “O roste sobstvennykh chisel lineinogo integralnogo uravneniya”, Vestn. MGU, 1966, no. 4, 3–19 | Zbl

[11] Kac M., “Distribution of eigenvalues of certain integral operators”, Michigan Math. J., 3 (1955–1956), 141–148 | DOI | MR

[12] Rosenblatt M., “Some results on the asymptotic behavior of eigenvalues for a class of integral equations with translation kernels”, J. Math., Mech., 12:4 (1963), 619–628 | MR | Zbl

[13] Widom H., “Asymptotic behavior of the eigenvalues of certain integral equations. II”, Arch. Rat. Mech., Anal., 17:3 (1964), 215–229 | DOI | MR | Zbl

[14] Krein M. G., “K teorii lineinykh nesamosopryazhennykh operatorov”, Dokl. AN SSSR, 130 (1960), 254–256 | MR | Zbl

[15] Gokhberg I. Ts., Krein M. G., Teoriya volterrovykh operatorov v gilbertovom prostranstve i ee prilozheniya, Nauka, M., 1967 | MR

[16] Evgrafov M. A., “Ob odnom integralnom preobrazovanii i o ego primenenii k otsenke chisla sobstvennykh znachenii nekotorykh integralnykh operatorov”, Tr. Mosk. matem. ob-va, 17 (1967), 273–292 | MR | Zbl

[17] Widom H., “Asymptotic behavior of the eigenvalues of certain integral equations. I”, Trans. Amer. Math. Soc., 109:2 (1963), 278–295 | DOI | MR | Zbl

[18] Gelfand I. M., Shilov G. E., Obobschennye funktsii, vyp. I, Fizmattiz, M., 1959

[19] Birman M. Sh., Solomyak M. Z., “Kusochno-polinomialnye priblizheniya funktsii klassov $W^\alpha_p$”, Matem. sb., 73 (1967), 331–355 | MR | Zbl

[20] Borzov V. V., “O kolichestvennykh kharakteristikakh singulyarnykh mer”, Problemy matematicheskoi fiziki, vyp. 4, LGU, 1970, 42–47 | MR