Multiplier (Fourier analysis)
In Fourier analysis, a multiplier operator is a type of linear operator, or transformation of functions. These operators act on a function by altering its Fourier transform. Specifically they multiply the Fourier transform of a function by a specified function known as the multiplier or symbol. Occasionally, the term multiplier operator itself is shortened simply to multiplier. In simple terms, the multiplier reshapes the frequencies involved in any function. This class of operators turns out to be broad: general theory shows that a translation-invariant operator on a group which obeys some (very mild) regularity conditions can be expressed as a multiplier operator, and conversely. Many familiar operators, such as translations and differentiation, are multiplier operators, although there a
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Andreas SeegerBochner–Riesz meanConvolutionDirac delta functionFourier multiplierFourier multiplier operatorFourier transformFractional LaplacianHeisenberg groupHilbert transformJózef MarcinkiewiczList of Fourier analysis topicsLittlewood–Paley theoryMarcinkiewicz interpolation theoremMarcinkiewicz multiplier theoremMultiplierMultiplier operatorMultiplier theoremPseudo-differential operatorRiemann–Liouville integralRiesz potentialRiesz transformRiesz–Thorin theoremSingular integralSingular integral operators of convolution typeSobolev spaceSolomon_MikhlinSpectral theoremSymbol of a differential operator
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Multiplier (Fourier analysis)
In Fourier analysis, a multiplier operator is a type of linear operator, or transformation of functions. These operators act on a function by altering its Fourier transform. Specifically they multiply the Fourier transform of a function by a specified function known as the multiplier or symbol. Occasionally, the term multiplier operator itself is shortened simply to multiplier. In simple terms, the multiplier reshapes the frequencies involved in any function. This class of operators turns out to be broad: general theory shows that a translation-invariant operator on a group which obeys some (very mild) regularity conditions can be expressed as a multiplier operator, and conversely. Many familiar operators, such as translations and differentiation, are multiplier operators, although there a
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In Fourier analysis, a multipl ...... es operator norm and Lp space.
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February 2017
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And are jump discontinuities at 2^ allowed?
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Hope this is right.
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In Fourier analysis, a multipl ...... er operators, although there a
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Multiplier (Fourier analysis)
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