| 1. | The derivative of a tempered distribution is again a tempered distribution.
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| 2. | The derivative of a tempered distribution is again a tempered distribution.
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| 3. | Where the limit is taken in the sense of tempered distributions.
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| 4. | The limit is written in various ways, often as a tempered distribution
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| 5. | Thus \ hat { \ delta } is defined as the unique tempered distribution satisfying
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| 6. | Exists as a tempered distribution for " f " a Schwartz function.
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| 7. | These spaces are spaces of measurable functions on when, and of tempered distributions on when.
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| 8. | In other words, a distribution " T " is a tempered distribution if and only if
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| 9. | Though conceptually different, the definition coincides with the one given later by Laurent Schwartz for tempered distributions.
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| 10. | The Fourier transform is a continuous, linear, bijective operator from the space of tempered distributions to itself.
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