Positive-definite Kernel - Definition

Definition

Let

be a sequence of (complex) Hilbert spaces and

be the bounded operators from Hi to Hj.

A map A on where

is called a positive definite kernel if for all m > 0 and, the following positivity condition holds:

Read more about this topic:  Positive-definite Kernel

Famous quotes containing the word definition:

    It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.
    François, Duc De La Rochefoucauld (1613–1680)

    One definition of man is “an intelligence served by organs.”
    Ralph Waldo Emerson (1803–1882)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)