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 first general store opened on the ‘Cold Saturday’ of the winter of 1833 ... Mrs. Mary Miller, daughter of the store’s promoter, recorded in a letter: ‘Chickens and birds fell dead from their roosts, cows ran bellowing through the streets’; but she failed to state what effect the freeze had on the gala occasion of the store opening.”
—Administration in the State of Sout, U.S. public relief program (1935-1943)
“We commonly say that the rich man can speak the truth, can afford honesty, can afford independence of opinion and action;—and that is the theory of nobility. But it is the rich man in a true sense, that is to say, not the man of large income and large expenditure, but solely the man whose outlay is less than his income and is steadily kept so.”
—Ralph Waldo Emerson (1803–1882)