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On a criterion for solvability of Fredholm equations
N. K. Al'bov
Abstract:
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.
Received: 22.05.1981 and 08.12.1983
Citation:
N. K. Al'bov, “On a criterion for solvability of Fredholm equations”, Math. USSR-Sb., 55:1 (1986), 113–119
Linking options:
https://www.mathnet.ru/eng/sm1960https://doi.org/10.1070/SM1986v055n01ABEH002994 https://www.mathnet.ru/eng/sm/v169/i1/p113
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Abstract page: | 369 | Russian version PDF: | 131 | English version PDF: | 15 | References: | 65 |
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