Timeline for Delta-distribution composed with a function from the Fourier representation
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 16, 2023 at 15:37 | comment | added | Tom Copeland | Composing the Dirac delta with functions is a common practice in physics. I related this trick to Laplace transforms to determine the Fuss-Catalan sequences in "Discriminating Deltas, Depressed Equations, and Generalized Catalan Numbers" tcjpn.files.wordpress.com/2013/04/discrdeltas9-6-20122.pdf. I think this might be extendable to general formal power series and a certain class of Laurent series, but that's a future project. | |
| Mar 16, 2023 at 13:48 | answer | added | memorial | timeline score: 1 | |
| Jan 14, 2019 at 20:11 | comment | added | reuns | What do you assume about $f$ ? That it is Schwartz, that $f$ and its Fourier transform are $L^1$ ? What do you assume about $\phi$ ? Let $T_n (x) = \int_{-n}^n e^{i xy}dy$, it converges to $\delta$ in the sense of distributions and $\int_0^x T_n(v)dv$ converges locally uniformly to $sign(x)$ away from $x =0$ and boundedly around $x=0$. Thus If $f\in C_c^0$ and $\phi $ is $C^1$ with no double zero and finitely zeros on each lnterval then $(T_n \circ \phi ,f ) \to( \delta\circ \phi ,f )$ | |
| Jan 14, 2019 at 16:34 | answer | added | mcd | timeline score: 5 | |
| Jan 14, 2019 at 14:25 | answer | added | Carlo Beenakker | timeline score: 2 | |
| Jan 14, 2019 at 13:39 | history | asked | BGJ | CC BY-SA 4.0 |