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 translation x ↦ f ( x + a ) . In time series analysis , the shift operator is called the lag operator .
28-557: (Redirected from SHIFT ) [REDACTED] Look up Shift or shift in Wiktionary, the free dictionary. Shift may refer to: Art, entertainment, and media [ edit ] Gaming [ edit ] Shift (series) , a 2008 online video game series by Armor Games Need for Speed: Shift , a 2009 racing video game Shift 2: Unleashed , its 2011 sequel Literature [ edit ] Shift (novel) ,
56-572: A 2009 racing video game Shift 2: Unleashed , its 2011 sequel Literature [ edit ] Shift (novel) , a 2010 alternative history book by Tim Kring and Dale Peck Shift (novella) , a 2013 science fiction book, part two of the Silo trilogy by Hugh Howey Shift the Ape , a character in The Chronicles of Narnia novel series Shift (DC Comics) , a DC Comics character who
84-518: A 2010 alternative history book by Tim Kring and Dale Peck Shift (novella) , a 2013 science fiction book, part two of the Silo trilogy by Hugh Howey Shift the Ape , a character in The Chronicles of Narnia novel series Shift (DC Comics) , a DC Comics character who is a fragment of Metamorpho Shift (Marvel Comics) , a Marvel Comics character who is a clone of Miles Morales Music [ edit ] Shift (Nasum album) , 2004 Shift (The Living End album) Shift (music) ,
112-505: A German company producing the Shiftphone SHIFT Inc. , a Japanese software testing company Linguistics [ edit ] Language shift , the process in which a community of speakers shift to speaking a different language Shifting (syntax) , a syntactic process Sound shift, also known as sound shifting or sound change Vowel shift Mathematics and computing [ edit ] Barrel shifter ,
140-433: A German company producing the Shiftphone SHIFT Inc. , a Japanese software testing company Linguistics [ edit ] Language shift , the process in which a community of speakers shift to speaking a different language Shifting (syntax) , a syntactic process Sound shift, also known as sound shifting or sound change Vowel shift Mathematics and computing [ edit ] Barrel shifter ,
168-687: A change of level in music Shift (string technique) , a finger movement from one position to another on the same string Other uses in arts, entertainment, and media [ edit ] Shift (magazine) , a former Canadian technology and culture magazine Shift (MSNBC) , an online live-streaming video network Shift (sculpture) , an outdoor sculpture by American artist Richard Serra located in King City, Ontario, Canada Business [ edit ] Shift work , an employment practice Shift (business) , an online peer-to-peer marketplace for buying and selling used cars SHIFT (company) ,
196-471: A defensive alignment in baseball and softball Other uses [ edit ] Shift (clothing) , a simple kind of undergarment or dress Shift (weapon) , an improvised knife used as a weapon Gear shift , a lever to change gear in a vehicle Paradigm shift , a change in basic assumptions within the ruling theory of science Blueshift , any decrease in wavelength, with a corresponding increase in frequency, of an electromagnetic wave Redshift ,
224-471: A defensive alignment in baseball and softball Other uses [ edit ] Shift (clothing) , a simple kind of undergarment or dress Shift (weapon) , an improvised knife used as a weapon Gear shift , a lever to change gear in a vehicle Paradigm shift , a change in basic assumptions within the ruling theory of science Blueshift , any decrease in wavelength, with a corresponding increase in frequency, of an electromagnetic wave Redshift ,
252-432: A digital circuit implementing bit shifts Bit shift , an operation treating a value as a sequence of binary digits Arithmetic shift Circular shift , often used in cryptography Logical shift Shift key , a key on a computer or typewriter keyboard Shift operator , a linear operator in mathematics Sports [ edit ] Shift (ice hockey) , a group of players in ice hockey Infield shift ,
280-432: A digital circuit implementing bit shifts Bit shift , an operation treating a value as a sequence of binary digits Arithmetic shift Circular shift , often used in cryptography Logical shift Shift key , a key on a computer or typewriter keyboard Shift operator , a linear operator in mathematics Sports [ edit ] Shift (ice hockey) , a group of players in ice hockey Infield shift ,
308-412: A former Canadian technology and culture magazine Shift (MSNBC) , an online live-streaming video network Shift (sculpture) , an outdoor sculpture by American artist Richard Serra located in King City, Ontario, Canada Business [ edit ] Shift work , an employment practice Shift (business) , an online peer-to-peer marketplace for buying and selling used cars SHIFT (company) ,
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#1732780767311336-839: A phenomenon that occurs when light seen coming from an object that is moving away is proportionally increased in wavelength, or shifted, to the red end of the spectrum Shapeshifting , a common theme in mythology, folklore, and fairy tales Shift vector, in ADM formalism of General Relativity Shifting, Hiberno-English slang for making out Tax shift , a fiscal policy See also [ edit ] [REDACTED] Search for "shift" or "shifts" on Misplaced Pages. All pages with titles beginning with Shift All pages with titles beginning with SHIFT All pages with titles containing shifts All pages with titles containing shift Shifter (disambiguation) The Shift (disambiguation) Topics referred to by
364-791: A phenomenon that occurs when light seen coming from an object that is moving away is proportionally increased in wavelength, or shifted, to the red end of the spectrum Shapeshifting , a common theme in mythology, folklore, and fairy tales Shift vector, in ADM formalism of General Relativity Shifting, Hiberno-English slang for making out Tax shift , a fiscal policy See also [ edit ] [REDACTED] Search for "shift" or "shifts" on Misplaced Pages. All pages with titles beginning with Shift All pages with titles beginning with SHIFT All pages with titles containing shifts All pages with titles containing shift Shifter (disambiguation) The Shift (disambiguation) Topics referred to by
392-411: Is a unitary operator on ℓ 2 ( Z ) . {\displaystyle \ell _{2}(\mathbb {Z} ).} The shift operator acting on functions of a real variable is a unitary operator on L 2 ( R ) . {\displaystyle L_{2}(\mathbb {R} ).} In both cases, the (left) shift operator satisfies
420-454: Is a fragment of Metamorpho Shift (Marvel Comics) , a Marvel Comics character who is a clone of Miles Morales Music [ edit ] Shift (Nasum album) , 2004 Shift (The Living End album) Shift (music) , a change of level in music Shift (string technique) , a finger movement from one position to another on the same string Other uses in arts, entertainment, and media [ edit ] Shift (magazine) ,
448-407: Is a function on an abelian group G , and h is an element of G , the shift operator T maps F to The shift operator acting on real- or complex-valued functions or sequences is a linear operator which preserves most of the standard norms which appear in functional analysis. Therefore, it is usually a continuous operator with norm one. The shift operator acting on two-sided sequences
476-415: Is a proper isometry with range equal to all vectors which vanish in the first coordinate . The operator S is a compression of T , in the sense that T − 1 y = S x for each x ∈ ℓ 2 ( N ) , {\displaystyle T^{-1}y=Sx{\text{ for each }}x\in \ell ^{2}(\mathbb {N} ),} where y
504-457: Is different from Wikidata All article disambiguation pages All disambiguation pages Shift [REDACTED] Look up Shift or shift in Wiktionary, the free dictionary. Shift may refer to: Art, entertainment, and media [ edit ] Gaming [ edit ] Shift (series) , a 2008 online video game series by Armor Games Need for Speed: Shift ,
532-582: Is different from Wikidata All article disambiguation pages All disambiguation pages Shift 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 . Shifts of sequences (functions of an integer variable) appear in diverse areas such as Hardy spaces ,
560-479: Is the vector in ℓ 2 ( Z ) {\displaystyle \ell _{2}(\mathbb {Z} )} with y i = x i for i ≥ 0 and y i = 0 for i < 0 . This observation is at the heart of the construction of many unitary dilations of isometries. The spectrum of S is the unit disk . The shift S is one example of a Fredholm operator ; it has Fredholm index −1. Jean Delsarte introduced
588-528: The flow and the group property completely determine the entire Lie flow, providing a solution to the translation functional equation The left shift operator acts on one-sided infinite sequence of numbers by and on two-sided infinite sequences by The right shift operator acts on one-sided infinite sequence of numbers by and on two-sided infinite sequences by The right and left shift operators acting on two-sided infinite sequences are called bilateral shifts. In general, as illustrated above, if F
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#1732780767311616-540: The following commutation relation with the Fourier transform: F T t = M t F , {\displaystyle {\mathcal {F}}T^{t}=M^{t}{\mathcal {F}},} where M is the multiplication operator by exp( itx ) . Therefore, the spectrum of T is the unit circle. The one-sided shift S acting on ℓ 2 ( N ) {\displaystyle \ell _{2}(\mathbb {N} )}
644-450: The linear operator T in terms of the plain derivative d d x {\displaystyle {\tfrac {d}{dx}}} was introduced by Lagrange , T t = e t d d x , {\displaystyle T^{t}=e^{t{\frac {d}{dx}}}~,} which may be interpreted operationally through its formal Taylor expansion in t ; and whose action on
672-1315: The monomial x is evident by the binomial theorem , and hence on all series in x , and so all functions f ( x ) as above. This, then, is a formal encoding of the Taylor expansion in Heaviside's calculus. The operator thus provides the prototype for Lie's celebrated advective flow for Abelian groups , where the canonical coordinates h ( Abel functions ) are defined such that For example, it easily follows that β ( x ) = x {\displaystyle \beta (x)=x} yields scaling, hence exp ( i π x d d x ) f ( x ) = f ( − x ) {\displaystyle \exp \left(i\pi x{\tfrac {d}{dx}}\right)f(x)=f(-x)} (parity); likewise, β ( x ) = x 2 {\displaystyle \beta (x)=x^{2}} yields β ( x ) = 1 x {\displaystyle \beta (x)={\tfrac {1}{x}}} yields β ( x ) = e x {\displaystyle \beta (x)=e^{x}} yields etc. The initial condition of
700-474: The notion of generalized shift operator (also called generalized displacement operator ); it was further developed by Boris Levitan . A family of operators { L x } x ∈ X {\displaystyle \{L^{x}\}_{x\in X}} acting on a space Φ of functions from a set X to C {\displaystyle \mathbb {C} }
728-407: The same term [REDACTED] This disambiguation page lists articles associated with the title Shift . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Shift&oldid=1239215730 " Category : Disambiguation pages Hidden categories: Short description
756-407: The same term [REDACTED] This disambiguation page lists articles associated with the title Shift . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Shift&oldid=1239215730 " Category : Disambiguation pages Hidden categories: Short description
784-543: 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. The shift operator T (where t ∈ R {\displaystyle t\in \mathbb {R} } ) takes a function f on R {\displaystyle \mathbb {R} } to its translation f t , A practical operational calculus representation of
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