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:
“You don’t want a general houseworker, do you? Or a traveling companion, quiet, refined, speaks fluent French entirely in the present tense? Or an assistant billiard-maker? Or a private librarian? Or a lady car-washer? Because if you do, I should appreciate your giving me a trial at the job. Any minute now, I am going to become one of the Great Unemployed. I am about to leave literature flat on its face. I don’t want to review books any more. It cuts in too much on my reading.”
—Dorothy Parker (1893–1967)
“The struggle for existence holds as much in the intellectual as in the physical world. A theory is a species of thinking, and its right to exist is coextensive with its power of resisting extinction by its rivals.”
—Thomas Henry Huxley (1825–95)