Fractional Calculus - Functional Calculus

Functional Calculus

In the context of functional analysis, functions f(D) more general than powers are studied in the functional calculus of spectral theory. The theory of pseudo-differential operators also allows one to consider powers of D. The operators arising are examples of singular integral operators; and the generalisation of the classical theory to higher dimensions is called the theory of Riesz potentials. So there are a number of contemporary theories available, within which fractional calculus can be discussed. See also Erdélyi–Kober operator, important in special function theory (Kober 1940), (Erdélyi 1950–51).

Read more about this topic:  Fractional Calculus

Famous quotes containing the words functional and/or calculus:

    Well designed, fully functional infant. Provides someone to live for as well as another mouth to feed. Produces cooing, gurgling and other adorable sounds. May cause similar behavior in nearby adults. Cries when hungry, sleepy or just because. Hand Wash with warm water and mild soap, then pat dry with soft cloth and talc. Internal mechanisms are self-cleaning... Two Genders: Male. Female. Five Colors: White. Black. Yellow. Red. Camouflage.
    Alfred Gingold, U.S. humorist. Items From Our Catalogue, “Baby,” Avon Books (1982)

    I try to make a rough music, a dance of the mind, a calculus of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.
    Judith Johnson Sherwin (b. 1936)