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- W306171216 abstract "A linear integral equation is an equation of the form $$begin{array}{*{20}{c}} {lambda a(x)varphi (x) - int_{x} {k(x,y)varphi (y)dv(y) = f(x)} ,} & {x in X.} end{array}$$(1)Here (X, v) is a measure space with σ-finite measure v, λ is a complex parameter, and a, k, f are given (complex-valued) functions, which are referred to as the coefficient, the kernel, and the free term (or the right-hand side) of equation (1), respectively. The problem consists in determining the parameter λ and the unknown function φ such that equation (1) is satisfied for almost all x ∈ X (or even for all x ∈ X if, for instance, the integral is understood in the sense of Riemann). In the case f = 0, the equation (1) is called homogeneous, otherwise it is called inhomogeneous. If a and k are matrix functions and, accordingly, φ and f are vector-valued functions, then (1) is referred to as a system of integral equations." @default.
- W306171216 created "2016-06-24" @default.
- W306171216 creator A5061294032 @default.
- W306171216 date "1991-01-01" @default.
- W306171216 modified "2023-09-24" @default.
- W306171216 title "Linear Integral Equations" @default.
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- W306171216 doi "https://doi.org/10.1007/978-3-642-58175-5_1" @default.
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