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- Fourier_inversion_theorem abstract "In mathematics, the Fourier inversion theorem says that for many types of function it is possible to recover a function from its Fourier transform. Intuitively it may be viewed as the statement that if we know all frequency and phase information about a wave then we may reconstruct the original wave precisely.The theorem says that if we have a function f: ℝn→ℂ satisfying certain conditions, and we use the convention for the Fourier transform that thenIn other words, the theorem says that This last equation is called the Fourier integral theorem.Another way to state the theorem is note that, if R is the flip operator i.e. Rf(x):=f(−x), then The theorem holds if both f and its Fourier transform are absolutely integrable (in the Lebesgue sense) and f is continuous at the point x. However, even under more general conditions versions of the Fourier inversion theorem hold. In these cases the integrals above may not make sense, or the theorem may hold for almost all x rather than for all x.".
- Fourier_inversion_theorem wikiPageID "382445".
- Fourier_inversion_theorem wikiPageRevisionID "603889099".
- Fourier_inversion_theorem hasPhotoCollection Fourier_inversion_theorem.
- Fourier_inversion_theorem subject Category:Generalized_functions.
- Fourier_inversion_theorem subject Category:Theorems_in_Fourier_analysis.
- Fourier_inversion_theorem type Abstraction100002137.
- Fourier_inversion_theorem type Communication100033020.
- Fourier_inversion_theorem type Function113783816.
- Fourier_inversion_theorem type GeneralizedFunctions.
- Fourier_inversion_theorem type MathematicalRelation113783581.
- Fourier_inversion_theorem type Message106598915.
- Fourier_inversion_theorem type Proposition106750804.
- Fourier_inversion_theorem type Relation100031921.
- Fourier_inversion_theorem type Statement106722453.
- Fourier_inversion_theorem type Theorem106752293.
- Fourier_inversion_theorem type TheoremsInFourierAnalysis.
- Fourier_inversion_theorem comment "In mathematics, the Fourier inversion theorem says that for many types of function it is possible to recover a function from its Fourier transform.".
- Fourier_inversion_theorem label "Fourier inversion theorem".
- Fourier_inversion_theorem label "Teorema di inversione di Fourier".
- Fourier_inversion_theorem sameAs Teorema_di_inversione_di_Fourier.
- Fourier_inversion_theorem sameAs m.021sbp.
- Fourier_inversion_theorem sameAs Q3984053.
- Fourier_inversion_theorem sameAs Q3984053.
- Fourier_inversion_theorem sameAs Fourier_inversion_theorem.
- Fourier_inversion_theorem wasDerivedFrom Fourier_inversion_theorem?oldid=603889099.
- Fourier_inversion_theorem isPrimaryTopicOf Fourier_inversion_theorem.