Homogeneous Wiener—Hopf Double Integral Equation with Symmetric Kernel in the Conservative Case
- Autores: Arabadzhyan L.G.1,2
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Afiliações:
- Institute of Mathematics
- Khachatur Abovian Armenian State Teachers’ Training University
- Edição: Volume 106, Nº 1-2 (2019)
- Páginas: 3-10
- Seção: Article
- URL: https://ogarev-online.ru/0001-4346/article/view/151799
- DOI: https://doi.org/10.1134/S0001434619070010
- ID: 151799
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Resumo
We establish nontrivial solvability conditions for the homogeneous double integral equation
\(S(x, y)=\int_{0}^{\infty} \int_{0}^{\infty} K\left(x-x^{\prime}, y-y^{\prime}\right) S\left(x^{\prime}, y^{\prime}\right) d x^{\prime} d y^{\prime}, \quad(x, y) \in \mathbb{R}_{+} \times \mathbb{R}_{+},\)![]()
where ℝ+ ≡ [0, +∞), under the assumption that the given function K satisfies the conservativity conditions \(0 \leq K \in L_{1}, \quad \iint_{\mathbb{R}^{2}} K(x, y) \ d x\ d y=1\)![]()
and some additional conditions on its first and second moments.Sobre autores
L. Arabadzhyan
Institute of Mathematics; Khachatur Abovian Armenian State Teachers’ Training University
Autor responsável pela correspondência
Email: arabajyan@mail.ru
Armênia, Yerevan, 375019; Yerevan, 375010
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