On Singular Normal Linear Integral Equations
Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 199-203
Voir la notice de l'article provenant de la source Cambridge University Press
In this work we consider the equation 1 where K(x, y) is singular in the sense that it does not properly belong to L 2 and f(x) is an arbitrary L 2 function.A Lebesgue measurable function K(x, y) of two variables, having real values on [0.1] × [0.1] is called a singular normal kernel of (i) There exists approximating kernels Km(x, y) satisfying (ii) (iii) (iv)
Costley, Charles G. On Singular Normal Linear Integral Equations. Canadian mathematical bulletin, Tome 13 (1970) no. 2, pp. 199-203. doi: 10.4153/CMB-1970-040-7
@article{10_4153_CMB_1970_040_7,
author = {Costley, Charles G.},
title = {On {Singular} {Normal} {Linear} {Integral} {Equations}},
journal = {Canadian mathematical bulletin},
pages = {199--203},
year = {1970},
volume = {13},
number = {2},
doi = {10.4153/CMB-1970-040-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1970-040-7/}
}
[1] 1. Goldfain, I. A., On a class of linear integral equations, Transi. Amer. Math. Soc. (2) 10 (1958), p. 283. Google Scholar
[2] 2. Carleman, T., Sur les équations intégrales singulières à Noyau Riel et symétrique, Uppsala, 1923. Google Scholar
[3] 3. Riesz, M. F., Uber Système Integrierbarer Funktionen, Math. Ann., 1910. Google Scholar
[4] 4. Stone, M. H., Linear transformation in Hilbert space, Amer. Math. Soc., Coll. XV, New York, 1932. Google Scholar
[5] 5. Trjitzinsky, W. J., Problems in the theory of integral equations, Ann. of Math., 1940. Google Scholar
Cité par Sources :