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:
“Where there is reverence there is fear, but there is not reverence everywhere that there is fear, because fear presumably has a wider extension than reverence.”
—Socrates (469–399 B.C.)
“Indigenous to Minnesota, and almost completely ignored by its people, are the stark, unornamented, functional clusters of concrete—Minnesota’s grain elevators. These may be said to express unconsciously all the principles of modernism, being built for use only, with little regard for the tenets of esthetic design.”
—Federal Writers’ Project Of The Wor, U.S. public relief program (1935-1943)
“Ask anyone committed to Marxist analysis how many angels on the head of a pin, and you will be asked in return to never mind the angels, tell me who controls the production of pins.”
—Joan Didion (b. 1934)