Definition:Integral Equation/Kernel
< Definition:Integral Equation(Redirected from Definition:Kernel of Integral Equation)
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Definition
Consider the integral equation:
- of the first kind:
- $\map f x = \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$
- of the second kind:
- $\map g x = \map f x + \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$
- of the third kind:
- $\map u x \map g x = \map f x + \lambda \ds \int_{\map a x}^{\map b x} \map K {x, y} \map g y \rd x$
The function $\map K {x, y}$ is known as the kernel of the integral equation.
Also see
- Results about integral equations can be found here.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): integral equation
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): integral equation