Far Eastern Mathematical Journal

To content of the issue


Fredholm formulae for kernels which are linear with respect to parameter


I. M. Novitskii

2002, issue 2, . 173194


Abstract
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

Keywords:

Download the article (PDF-file)

References

[1] Anthony F. Ruston, Fredholm theory in Banach spaces, Cambridge Univ. Press, Cambridge e.a., 1986.
[2] I. Fredholm, Sur une classe d'e?quations fonctionnelles, Acta math., 27 (1903), 365390.
[3] I. Fredholm, Letter to G. MittagLeffler. August 8, 1899, Uvres Comple?tes de Ivar Fredholm, Litos Reprotryck, Malmo?, 1955.
[4] I. M. Novickij, O minorax Fredgol'ma dlya vpolne nepreryvnyx operatorov, Dal'nevostochnyj matematicheskij sbornik, 7, 1999, 103122.
[5] I. M. Novickij, Privedenie linejnyx operatorov v $L_2$ k integral'nomu vidu s gladkimi yadrami, Dokl. AN SSSR, 318:5 (1991), 10881091.
[6] I. M. Novickij, Simultaneous unitary equivalence of operators families to integral operators with smooth kernels and its applications, Preprint instituta prikladnoj matematiki, DVO AN SSSR, Vladivostok, 1990, 29 s.
[7] N. I. Axiezer, I. M. Glazman, Teoriya linejnyx operatorov v gil'bertovom prostranstve, Nauka, M., 1966.
[8] I. M. Novitskii?\, Integral representations of linear operators by smooth Carleman kernels of Mercer type, Proc. London Math. Soc. III ser., 68:1 (1994), 161177.
[9] M. Markus, Ch. Mink, Obzor po teorii matric i matrichnyx neravenstv, Nauka, M., 1972.

To content of the issue