Function Space - Functional Analysis

Functional Analysis

Functional analysis is organized around adequate techniques to bring function spaces as topological vector spaces within reach of the ideas that would apply to normed spaces of finite dimension.

  • Schwartz space of smooth functions of rapid decrease and its dual, tempered distributions
  • Lp space
  • κ(R) continuous functions with compact support endowed with the uniform norm topology
  • B(R) bounded continuous (Bounded function)
  • C∞(R) continuous functions which vanish at infinity
  • Cr(R) continuous functions that have continuous first r derivatives.
  • C∞(R) Smooth functions
  • C∞c smooth functions with compact support
  • D(R) compact support in limit topology
  • Wk,p Sobolev space
  • OU holomorphic functions
  • linear functions
  • piecewise linear functions
  • continuous functions, compact open topology
  • all functions, space of pointwise convergence
  • Hardy space
  • Hölder space
  • Càdlàg functions, also known as the Skorokhod space

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