Global Information Lookup Global Information

Shift operator information


In mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function xf(x) to its translation xf(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.

  1. ^ Weisstein, Eric W. "Shift Operator". MathWorld.
  2. ^ 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.

and 21 Related for: Shift operator information

Request time (Page generated in 0.8293 seconds.)

Shift operator

Last Update:

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 translation...

Word Count : 1452

Bitwise operation

Last Update:

"<<<" operator in Java. More details of Java shift operators: The operators << (left shift), >> (signed right shift), and >>> (unsigned right shift) are...

Word Count : 3812

Bitwise operations in C

Last Update:

01110000 There are two bitwise shift operators. They are Right shift (>>) Left shift (<<) The symbol of right shift operator is >>. For its operation, it...

Word Count : 1863

Arithmetic shift

Last Update:

In computer programming, an arithmetic shift is a shift operator, sometimes termed a signed shift (though it is not restricted to signed operands). The...

Word Count : 1716

Logical shift

Last Update:

logical right shift operator is >>>, but the arithmetic right shift operator is >>. (Java has only one left shift operator (<<), because left shift via logic...

Word Count : 627

Shift

Last Update:

cryptography Logical shift Shift key, a key on a computer keyboard or typewriter Shift operator, a linear operator in mathematics Shift (ice hockey), a group...

Word Count : 492

Delta operator

Last Update:

In mathematics, a delta operator is a shift-equivariant linear operator Q : K [ x ] ⟶ K [ x ] {\displaystyle Q\colon \mathbb {K} [x]\longrightarrow \mathbb...

Word Count : 619

Displacement operator

Last Update:

mechanics study of optical phase space, the displacement operator for one mode is the shift operator in quantum optics, D ^ ( α ) = exp ⁡ ( α a ^ † − α ∗...

Word Count : 725

Composition operator

Last Update:

When the transfer operator is a left-shift operator, the Koopman operator, as its adjoint, can be taken to be the right-shift operator. An appropriate basis...

Word Count : 730

Jacobi operator

Last Update:

the Hessenberg operator that generalizes the tridiagonal Jacobi operator J for this situation. Note that D is the right-shift operator on the Bergman...

Word Count : 790

Operator theory

Last Update:

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

Word Count : 1543

Transfer operator

Last Update:

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...

Word Count : 797

Fredholm operator

Last Update:

The (right) shift operator 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...

Word Count : 1472

Bernoulli scheme

Last Update:

to that of the Bernoulli shift. This is essentially the Markov partition. The term shift is in reference to the shift operator, which may be used to study...

Word Count : 1739

Delimited continuation

Last Update:

offers two control operators, shift and reset, that give rise to static rather than to dynamic delimited continuations. The reset operator sets the limit...

Word Count : 1344

Optical phase space

Last Update:

illustrates the effects of the phase-shifting operator on coherent states. The displacement operator is a unitary operator that takes a coherent state and...

Word Count : 2494

Lag operator

Last Update:

Autoregressive model Autoregressive moving average model Moving average model Shift operator Z-transform Hamilton, James Douglas (1994). Time Series Analysis. Princeton...

Word Count : 938

Translation operator

Last Update:

Translation operator can refer to these things: Translation operator (quantum mechanics) Shift operator, which effects a geometric translation Translation...

Word Count : 57

Unitary operator

Last Update:

dimensional case, such operators are the permutation matrices. The unilateral shift (right shift) is an isometry; its conjugate (left shift) is a coisometry...

Word Count : 1263

Subshift of finite type

Last Update:

j\in \mathbb {Z} \right\}.} The shift operator T maps a sequence in the one- or two-sided shift to another by shifting all symbols to the left, i.e. (...

Word Count : 2380

Multiplication operator

Last Update:

multiplication operator on any Lp space. Translation operator Shift operator Transfer operator Decomposition of spectrum (functional analysis) Conway...

Word Count : 360

PDF Search Engine © AllGlobal.net