Extension To Functional Analysis
The concept of a holomorphic function can be extended to the infinite-dimensional spaces of functional analysis. For instance, the Fréchet or Gâteaux derivative can be used to define a notion of a holomorphic function on a Banach space over the field of complex numbers.
Read more about this topic: Holomorphic Function
Famous quotes containing the words extension, functional and/or analysis:
“Slavery is founded on the selfishness of man’s nature—opposition to it on his love of justice. These principles are in eternal antagonism; and when brought into collision so fiercely as slavery extension brings them, shocks and throes and convulsions must ceaselessly follow.”
—Abraham Lincoln (1809–1865)
“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)
“... the big courageous acts of life are those one never hears of and only suspects from having been through like experience. It takes real courage to do battle in the unspectacular task. We always listen for the applause of our co-workers. He is courageous who plods on, unlettered and unknown.... In the last analysis it is this courage, developing between man and his limitations, that brings success.”
—Alice Foote MacDougall (1867–1945)