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:
“A dense undergrowth of extension cords sustains my upper world of lights, music, and machines of comfort.”
—Mason Cooley (b. 1927)
“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)
“... 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)