Further Examples
The following table shows some common examples of multiplier operators on the unit circle .
Name | Multiplier | Operator | Kernel |
---|---|---|---|
Identity operator | 1 | f(t) | Dirac delta function |
Multiplication by a constant c | c | cf(t) | |
Translation by s | f(t − s) | ||
Differentiation | in | f '(t) | |
k-fold differentiation | |||
Constant coefficient differential operator | |||
Fractional derivative of order | |||
Mean value | 1 | ||
Mean-free component | |||
Integration (of mean-free component) | Sawtooth function | ||
Periodic Hilbert transform H | |||
Dirichlet summation | Dirichlet kernel | ||
Fejér summation | Fejér kernel | ||
General multiplier | |||
General convolution operator |
The following table shows some common examples of multiplier operators on Euclidean space .
Name | Multiplier | Operator | Kernel |
---|---|---|---|
Identity operator | 1 | f(x) | |
Multiplication by a constant c | c | cf(x) | |
Translation by y | f(x − y) | ||
Derivative (one dimension only) | |||
Partial derivative | |||
Laplacian | |||
Constant coefficient differential operator | |||
Fractional derivative of order | |||
Riesz potential of order | |||
Bessel potential of order | |||
Heat flow operator | Heat kernel | ||
Schrödinger equation evolution operator | Schrödinger kernel | ||
Hilbert transform H (one dimension only) | |||
Riesz transforms Rj | |||
Partial Fourier integral (one dimension only) | |||
Disk multiplier | (J is a Bessel function) | ||
Bochner–Riesz operators | |||
General multiplier | |||
General convolution operator |
Read more about this topic: Multiplier (Fourier Analysis)
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