Linear mathematical operator which translates a function
This article is about shift operators in mathematics. For operators in computer programming languages, see Bit shift. For the shift operator of group schemes, see Verschiebung operator.
In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f(x)
to its translationx ↦ f(x + a).[1] 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 functions, positive-definite functions, derivatives, and convolution.[2] Shifts of sequences (functions of an integer variable) appear 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. The notion of triangulated category is a categorified analogue of the shift operator.
^Weisstein, Eric W. "Shift Operator". MathWorld.
^Marchenko, V. A. (2006). "The generalized shift, transformation operators, and inverse problems". Mathematical events of the twentieth century. Berlin: Springer. pp. 145–162. doi:10.1007/3-540-29462-7_8. ISBN 978-3-540-23235-3. MR 2182783.
in particular functional analysis, the shiftoperator, also known as the translation operator, is an operator that takes a function x ↦ f(x) to its translation...
"<<<" operator in Java. More details of Java shiftoperators: The operators << (left shift), >> (signed right shift), and >>> (unsigned right shift) are...
01110000 There are two bitwise shiftoperators. They are Right shift (>>) Left shift (<<) The symbol of right shiftoperator is >>. For its operation, it...
In computer programming, an arithmetic shift is a shiftoperator, sometimes termed a signed shift (though it is not restricted to signed operands). The...
cryptography Logical shiftShift key, a key on a computer keyboard or typewriter Shiftoperator, a linear operator in mathematics Shift (ice hockey), a group...
logical right shiftoperator is >>>, but the arithmetic right shiftoperator is >>. (Java has only one left shiftoperator (<<), because left shift via logic...
In mathematics, a delta operator is a shift-equivariant linear operator Q : K [ x ] ⟶ K [ x ] {\displaystyle Q\colon \mathbb {K} [x]\longrightarrow \mathbb...
mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...
When the transfer operator is a left-shiftoperator, the Koopman operator, as its adjoint, can be taken to be the right-shiftoperator. An appropriate basis...
the Hessenberg operator that generalizes the tridiagonal Jacobi operator J for this situation. Note that D is the right-shiftoperator on the Bergman...
mechanics study of optical phase space, the displacement operator for one mode is the shiftoperator in quantum optics, D ^ ( α ) = exp ( α a ^ † − α ∗...
The (right) shiftoperator S on H is defined by S ( e n ) = e n + 1 , n ≥ 0. {\displaystyle S(e_{n})=e_{n+1},\quad n\geq 0.\,} This operator S is injective...
Translation operator can refer to these things: Translation operator (quantum mechanics) Shiftoperator, which effects a geometric translation Translation...
the transfer operator can usually be interpreted as a (left-)shiftoperator acting on a shift space. The most commonly studied shifts are the subshifts...
Autoregressive model Autoregressive moving average model Moving average model Shiftoperator Z-transform Hamilton, James Douglas (1994). Time Series Analysis. Princeton...
illustrates the effects of the phase-shiftingoperator on coherent states. The displacement operator is a unitary operator that takes a coherent state and...
In functional analysis and operator theory, a bounded linear operator is a linear transformation L : X → Y {\displaystyle L:X\to Y} between topological...
to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shiftoperator, which may be used to study...
offers two control operators, shift and reset, that give rise to static rather than to dynamic delimited continuations. The reset operator sets the limit...
dimensional case, such operators are the permutation matrices. The unilateral shift (right shift) is an isometry; its conjugate (left shift) is a coisometry...
multiplication operator on any Lp space. Translation operatorShiftoperator Transfer operator Decomposition of spectrum (functional analysis) Arveson...
j\in \mathbb {Z} \right\}.} The shiftoperator T maps a sequence in the one- or two-sided shift to another by shifting all symbols to the left, i.e. (...
Global Information