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:
“There is in general good reason to suppose that in several respects the gods could all benefit from instruction by us human beings. We humans are—more humane.”
—Friedrich Nietzsche (1844–1900)
“No theory is good unless it permits, not rest, but the greatest work. No theory is good except on condition that one use it to go on beyond.”
—André Gide (1869–1951)