Theorems in functional analysis | C*-algebras | Invariant subspaces | Operator theory

Wold's decomposition

In mathematics, particularly in operator theory, Wold decomposition or Wold–von Neumann decomposition, named after Herman Wold and John von Neumann, is a classification theorem for isometric linear operators on a given Hilbert space. It states that every isometry is a direct sum of copies of the unilateral shift and a unitary operator. In time series analysis, the theorem implies that any stationary discrete-time stochastic process can be decomposed into a pair of uncorrelated processes, one deterministic, and the other being a moving average process. (Wikipedia).

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Related pages

Compact operator on Hilbert space | Operator theory | Hilbert space | Stationary process | Toeplitz algebra | Mathematics | Spectrum (functional analysis) | Wandering set | Unitary operator | Isometry | Stochastic process | Toeplitz operator | C*-algebra | John von Neumann | Continuous functional calculus