Difference between revisions of "Linear integral equation"
From Encyclopedia of Mathematics
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| − | An integral equation in which the unknown function | + | {{TEX|done}} |
| + | An integral equation in which the unknown function $\phi(s)$ occurs in a linear fashion: | ||
| − | + | $$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$ | |
| − | Here | + | Here $A$, $K$, $f$ are given functions, $D$ is a domain of the Euclidean space, $k$ and $s$ are points of the space, and $ds$ is the volume element. For more details see [[Integral equation|Integral equation]]. |
Latest revision as of 16:46, 7 July 2014
An integral equation in which the unknown function $\phi(s)$ occurs in a linear fashion:
$$A(x)\phi(x)+\int\limits_DK(x,s)\phi(s)ds=f(x),\quad x\in D.$$
Here $A$, $K$, $f$ are given functions, $D$ is a domain of the Euclidean space, $k$ and $s$ are points of the space, and $ds$ is the volume element. For more details see Integral equation.
How to Cite This Entry:
Linear integral equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_integral_equation&oldid=18296
Linear integral equation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Linear_integral_equation&oldid=18296
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article