tempered distribution वाक्य
उदाहरण वाक्य
मोबाइल
- The derivative of a tempered distribution is again a tempered distribution.
- The derivative of a tempered distribution is again a tempered distribution.
- Where the limit is taken in the sense of tempered distributions.
- The limit is written in various ways, often as a tempered distribution
- Thus \ hat { \ delta } is defined as the unique tempered distribution satisfying
- Exists as a tempered distribution for " f " a Schwartz function.
- These spaces are spaces of measurable functions on when, and of tempered distributions on when.
- In other words, a distribution " T " is a tempered distribution if and only if
- Though conceptually different, the definition coincides with the one given later by Laurent Schwartz for tempered distributions.
- The Fourier transform is a continuous, linear, bijective operator from the space of tempered distributions to itself.
- This version of the theorem is used in the proof of the Fourier inversion theorem for tempered distributions ( see below ).
- The space of "'tempered distributions "'is defined as the ( continuous ) dual of the Schwartz space.
- A precise version of this result, given below, holds for distributions of compact support, tempered distributions, and general distributions.
- There, it is explained that the sum of exponentials only agrees with the sum of deltas in the sense of tempered distributions.
- Therefore, this map defines, as it is obviously linear, a continuous functional on the Schwartz space and therefore a tempered distribution.
- For the definition of the Fourier transform of a tempered distribution, let and be integrable functions, and let and be their Fourier transforms respectively.
- Tempered distributions generalize the bounded ( or slow-growing ) locally integrable functions; all distributions with compact support and all square-integrable functions are tempered distributions.
- Tempered distributions generalize the bounded ( or slow-growing ) locally integrable functions; all distributions with compact support and all square-integrable functions are tempered distributions.
- Generally, the Fourier transform can be defined for any tempered distribution; moreover, any distribution of compact support " v " is a tempered distribution.
- Generally, the Fourier transform can be defined for any tempered distribution; moreover, any distribution of compact support " v " is a tempered distribution.
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