Integral Equations
Let be an integral kernel, and consider the homogeneous equation, the Fredholm integral equation,
and the inhomogeneous equation
The Fredholm alternative states that, for any non-zero fixed complex number, either the first equation has a non-trivial solution, or the second equation has a solution for all .
A sufficient condition for this theorem to hold is for to be square integrable on the rectangle (where a and/or b may be minus or plus infinity).
Read more about this topic: Fredholm Alternative
Famous quotes containing the word integral:
“Make the most of your regrets; never smother your sorrow, but tend and cherish it till it come to have a separate and integral interest. To regret deeply is to live afresh.”
—Henry David Thoreau (1817–1862)