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 March 31st, 2018, 02:24 PM #1 Newbie   Joined: Mar 2018 From: DK Posts: 1 Thanks: 0 Distribution - Fourier series Good day, I am trying to solve an exercise in the course of distribution theory and fourier analysis. I am new to the matter of using distribution in calculating, and I am thankful for any help to solve the following question: 1. Consider the $2\pi$ -periodic function $f(x)$ defined on $[0,2\pi)$ by $f(x)=\frac{1}{2}(\pi-x)$. prove (by calculating the Fourier series) that in the sense of distributions $\sum_{n=1}^{\infty }\frac{sin(nx)}{n}=f(x)$. 2. prove that-in the sense of distributions $\sum_{n\in \mathbb{Z}}e^{inx}=2\pi\sum_{n\in \mathbb{Z}}\delta_{2\pi n}$ in $D^{'}(\mathbb{R})$ Where $\delta_{2\pi n}$ is the distribution $\phi \mapsto \phi (2 \pi n)$ Thanks. Tags distribution, fourier, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post zollen Linear Algebra 9 March 7th, 2018 02:26 PM rodneyq Differential Equations 1 December 2nd, 2015 06:31 AM elena1 Calculus 5 December 19th, 2014 05:47 AM griglo Real Analysis 2 October 23rd, 2012 06:22 AM arron1990 Applied Math 1 August 10th, 2012 02:55 AM

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