Geodesic
Fredholm formulae for kernels which are linear with respect to parameter
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 173-194 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we construct formulae, which are similar to the classical determinant formulae of Fredholm, for solving second-kind integral equations in $L_2(\mathbb R)$ with continuous on $\mathbb R^2$ Carleman kernels of the form $H(s,t)+\mu G(s,t)$, where $\mu$ is a complex parameter 
@article{DVMG_2002_3_2_a3,
     author = {I. M. Novitskii},
     title = {Fredholm formulae for kernels which are linear with respect to parameter},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {173--194},
     year = {2002},
     volume = {3},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/}
}
TY  - JOUR
AU  - I. M. Novitskii
TI  - Fredholm formulae for kernels which are linear with respect to parameter
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2002
SP  - 173
EP  - 194
VL  - 3
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/
LA  - ru
ID  - DVMG_2002_3_2_a3
ER  - 
%0 Journal Article
%A I. M. Novitskii
%T Fredholm formulae for kernels which are linear with respect to parameter
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2002
%P 173-194
%V 3
%N 2
%U http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/
%G ru
%F DVMG_2002_3_2_a3
I. M. Novitskii. Fredholm formulae for kernels which are linear with respect to parameter. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 2, pp. 173-194. http://geodesic.mathdoc.fr/item/DVMG_2002_3_2_a3/

[1] Anthony F. Ruston, Fredholm theory in Banach spaces, Cambridge Univ. Press, Cambridge e.a., 1986 | MR

[2] I. Fredholm, “Sur une classe d'équations fonctionnelles”, Acta math., 27 (1903), 365–390 | DOI | MR | Zbl

[3] I. Fredholm, Letter to G. Mittag–Leffler. August 8, 1899, Uvres Complètes de Ivar Fredholm, Litos Reprotryck, Malmö, 1955

[4] I. M. Novitskii, “O minorakh Fredgolma dlya vpolne nepreryvnykh operatorov”, Dalnevostochnyi matematicheskii sbornik, 7, 1999, 103–122

[5] I. M. Novitskii, “Privedenie lineinykh operatorov v $L_2$ k integralnomu vidu s gladkimi yadrami”, Dokl. AN SSSR, 318:5 (1991), 1088–1091 | MR

[6] I. M. Novitskii, Simultaneous unitary equivalence of operators families to integral operators with smooth kernels and its applications, Preprint instituta prikladnoi matematiki, DVO AN SSSR, Vladivostok, 1990, 29 pp.

[7] N. I. Akhiezer, I. M. Glazman, Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1966 | MR | Zbl

[8] I. M. Novitskiĭ\, “Integral representations of linear operators by smooth Carleman kernels of Mercer type”, Proc. London Math. Soc. III ser., 68:1 (1994), 161–177 | MR | Zbl

[9] M. Markus, Ch. Mink, Obzor po teorii matrits i matrichnykh neravenstv, Nauka, M., 1972 | MR