High Quality Content by WIKIPEDIA articles! In mathematics, and in particular functional analysis, the shift operators are examples of linear operators, important for their simplicity and natural occurrence. They are used in diverse areas, such as Hardy spaces, the theory of abelian varieties, and the theory of symbolic dynamics, for which the baker's map is an explicit representation. (There is another usage of shift operator as a translation operator: see for example Sheffer sequence.) In time series analysis, this operator is called the lag operator.

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