General Theory
The general theory underlying the Fredholm equations is known as Fredholm theory. One of the principal results is that the kernel K is a compact operator, known as the Fredholm operator. Compactness may be shown by invoking equicontinuity. As an operator, it has a spectral theory that can be understood in terms of a discrete spectrum of eigenvalues that tend to 0.
Read more about this topic: Fredholm Integral Equation
Famous quotes containing the words general and/or theory:
“The General Order is always to manoeuver in a body and on the attack; to maintain strict but not pettifogging discipline; to keep the troops constantly at the ready; to employ the utmost vigilance on sentry go; to use the bayonet on every possible occasion; and to follow up the enemy remorselessly until he is utterly destroyed.”
—Lazare Carnot (1753–1823)
“Frankly, these days, without a theory to go with it, I can’t see a painting.”
—Tom Wolfe (b. 1931)