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:
“In former times and in less complex societies, children could find their way into the adult world by watching workers and perhaps giving them a hand; by lingering at the general store long enough to chat with, and overhear conversations of, adults...; by sharing and participating in the tasks of family and community that were necessary to survival. They were in, and of, the adult world while yet sensing themselves apart as children.”
—Dorothy H. Cohen (20th century)
“The human species, according to the best theory I can form of it, is composed of two distinct races, the men who borrow and the men who lend.”
—Charles Lamb (1775–1834)