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:
“I suggested to them also the great desirability of a general knowledge on the Island of the English language. They are under an English speaking government and are a part of the territory of an English speaking nation.... While I appreciated the desirability of maintaining their grasp on the Spanish language, the beauty of that language and the richness of its literature, that as a practical matter for them it was quite necessary to have a good comprehension of English.”
—Calvin Coolidge (1872–1933)
“Hygiene is the corruption of medicine by morality. It is impossible to find a hygienest who does not debase his theory of the healthful with a theory of the virtuous.... The true aim of medicine is not to make men virtuous; it is to safeguard and rescue them from the consequences of their vices.”
—H.L. (Henry Lewis)