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In time series analysis, the shift operator is called the lag operator. Shift operators are examples of linear operators, important for their simplicity and natural occurrence. The shift operator action on functions of a real variable plays an important role in harmonic analysis, for example, it appears in the definitions of almost periodic ...
("Verschiebung" is German for "shift", but the term "Verschiebung" is often used for this operator even in other languages.) The Verschiebung operator V and the Frobenius operator F are related by FV = VF = [ p ], where [ p ] is the p th power homomorphism of an abelian group scheme.
In mathematics, a generalized Clifford algebra (GCA) is a unital associative algebra that generalizes the Clifford algebra, and goes back to the work of Hermann Weyl, [1] who utilized and formalized these clock-and-shift operators introduced by J. J. Sylvester (1882), [2] and organized by Cartan (1898) [3] and Schwinger.
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The left-adjoint of the Perron–Frobenius operator is the Koopman operator or composition operator. The general setting is provided by the Borel functional calculus. As a general rule, the transfer operator can usually be interpreted as a (left-)shift operator acting on a shift space. The most commonly studied shifts are the subshifts of ...
Various operators for delimited continuations have been proposed in the research literature. [8]One independent proposal [5] is based on continuation-passing style (CPS) -- i.e., not on continuation frames—and offers two control operators, shift and reset, that give rise to static rather than to dynamic delimited continuations. [9]
The eigenvalues form a discrete spectrum, when the operator is limited to act on functions on the unit interval of the real number line. More broadly, since the Gauss map is the shift operator on Baire space, the GKW operator can also be viewed as an operator on the function space (considered as a Banach space, with basis functions taken to be the indicator functions on the cylinders of the ...
The formal definition of an arithmetic shift, from Federal Standard 1037C is that it is: . A shift, applied to the representation of a number in a fixed radix numeration system and in a fixed-point representation system, and in which only the characters representing the fixed-point part of the number are moved.
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