Editing Norbert Wiener (section)

===In mathematics ===
Wiener took a great interest in the mathematical theory of [[Brownian motion]] (named after [[Robert Brown (Scottish botanist from Montrose)|Robert Brown]]) proving many results now widely known, such as the non-differentiability of the paths. Consequently, the one-dimensional version of Brownian motion was named the [[Wiener process]]. It is the best known of the [[Lévy process]]es, [[càdlàg]] stochastic processes with stationary statistically [[independent increments]], and occurs frequently in pure and applied mathematics, physics and economics (e.g. on the stock-market).

[[Wiener's tauberian theorem]], a 1932 result of Wiener, developed [[Tauberian theorem]]s in [[summability theory]], on the face of it a chapter of [[real analysis]], by showing that most of the known results could be encapsulated in a principle taken from [[harmonic analysis]]. In its present formulation, the theorem of Wiener does not have any obvious association with Tauberian theorems, which deal with [[infinite series]]; the translation from results formulated for integrals, or using the language of [[functional analysis]] and [[Banach algebra]]s, is however a relatively routine process.

The [[Paley–Wiener theorem]] relates growth properties of [[entire function]]s on '''C'''<sup>n</sup> and Fourier transformation of Schwartz distributions of compact support.

The [[Wiener–Khinchin theorem]], (also known as the ''Wiener – Khintchine theorem'' and the ''Khinchin – Kolmogorov theorem''), states that the power spectral density of a wide-sense-stationary random process is the Fourier transform of the corresponding autocorrelation function.

An [[abstract Wiener space]] is a mathematical object in [[measure theory]], used to construct a "decent", strictly positive and locally finite measure on an infinite-dimensional vector space. Wiener's original construction only applied to the space of real-valued continuous paths on the unit interval, known as [[classical Wiener space]]. Leonard Gross provided the generalization to the case of a general [[separable space|separable]] [[Banach space]].

The notion of a Banach space itself was discovered independently by both Wiener and [[Stefan Banach]] at around the same time.<ref>{{cite journal |last1=Wiener |first1=Norbert |year=1923 |title=Note on a paper of M. Banach |journal=Fund. Math. |volume=4 |pages=136–143 |doi=10.4064/fm-4-1-136-143 |doi-access=free }}
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{{cite book |last1=Albiac |first1=F. |last2=Kalton |first2=N. |author2-link=Nigel Kalton |year=2006 |title=Topics in Banach Space Theory |publisher=Springer |location=New York, NY |isbn=978-0-387-28141-4 |page=15 |series=[[Graduate Texts in Mathematics]] |volume=233 }}</ref>