Geodesic
On a criterion for solvability of Fredholm equations
Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 113-119 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Fredholm equations of the first and second kinds are considered in an abstract Hilbert space. A unified solvability criterion is given for them in terms of nonnegativity of bilinear forms. For Fredholm equations of the second kind it is possible to pass from an arbitrary equation to an equation with nonnegative operator, some solution of which can be used to construct a solution of the original equation that is minimal in norm. Questions connected with restrictions on the norms of solutions are answered for these equations. The results are then carried over to Fredholm integral equations of both kinds and to linear algebraic systems. Bibliography: 4 titles. 
@article{SM_1986_55_1_a6,
     author = {N. K. Al'bov},
     title = {On a~criterion for solvability of {Fredholm} equations},
     journal = {Sbornik. Mathematics},
     pages = {113--119},
     year = {1986},
     volume = {55},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_55_1_a6/}
}
TY  - JOUR
AU  - N. K. Al'bov
TI  - On a criterion for solvability of Fredholm equations
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 113
EP  - 119
VL  - 55
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1986_55_1_a6/
LA  - en
ID  - SM_1986_55_1_a6
ER  - 
%0 Journal Article
%A N. K. Al'bov
%T On a criterion for solvability of Fredholm equations
%J Sbornik. Mathematics
%D 1986
%P 113-119
%V 55
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1986_55_1_a6/
%G en
%F SM_1986_55_1_a6
N. K. Al'bov. On a criterion for solvability of Fredholm equations. Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 113-119. http://geodesic.mathdoc.fr/item/SM_1986_55_1_a6/

[1] Efimov A. V., Potapov V. P., “$J$-rastyagivayuschie matritsy-funktsii i ikh rol v analiticheskoi teorii el. tsepei”, UMN, 28:1 (1973), 65–130 | MR | Zbl

[2] Krein S. G., Lineinye uravneniya v banakhovom prostranstve, Nauka, M., 1971 | MR

[3] Akhiezer N. I., Glazman I. M., Teoriya lineinykh operatorov v gilbertovom prostranstve, Nauka, M., 1972

[4] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1968, s. 449–468 | MR | Zbl