Category:Tuning Fork Delta Sequence
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This category contains pages concerning Tuning Fork Delta Sequence:
Let $\sequence {\map {\delta_n} x}$ be a sequence such that:
- $\map {\delta_n} x := \begin{cases} -n & : \size x < \frac 1 {2n} \\ 2n & : \frac 1 {2n} \le \size x \le \frac 1 n \\ 0 & : \size x > \frac 1 n \end{cases}$
Then $\sequence {\map {\delta_n} x}_{n \mathop \in {\N_{>0} } }$ is a delta sequence.
That is, in the distributional sense it holds that:
- $\ds \lim_{n \mathop \to \infty} \map {\delta_n} x = \map \delta x$
or
- $\ds \lim_{n \mathop \to \infty} \int_{-\infty}^\infty \map {\delta_n} x \map \phi x \rd x = \map \delta \phi$
where $\phi \in \map \DD \R$ is a test function, $\delta$ is the Dirac delta distribution, and $\map \delta x$ is the abuse of notation, usually interpreted as an infinitely thin and tall spike with its area equal to $1$.
Pages in category "Tuning Fork Delta Sequence"
The following 3 pages are in this category, out of 3 total.