Nicolas Essis-Breton
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 Oct 18 asked If $f$ is absolutely continuous then $\sum|\hat f (n) | < \infty$ Oct 16 accepted Find the rate of growth for $\sum_{n=1}^N 1/n^p$ in term of big $O$ notation Oct 16 asked Find the rate of growth for $\sum_{n=1}^N 1/n^p$ in term of big $O$ notation Oct 16 comment Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition I amended the title to match the question. Thank you very much. Oct 16 revised Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition amend title, to math previous body edit Oct 16 accepted Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition Oct 16 revised Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition per robert comment Oct 16 comment Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition @RobertIsrael I see your point, I relax this requirement in the question. However, as $x_n$ is a decreasing sequence, I think your example doesn't apply, but your point is still valid. Oct 16 revised Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition edit per Robert comment Oct 16 accepted Derivating $f(t)=\int_0^t x dx$ using measure theory Oct 16 accepted Convergence of the Fourier series of $f(t)=(t-\pi)\chi_{\left(0,2\pi\right)}$ Oct 16 asked Show from every positive sequence decreasing to zero, we can build a sequence satisfying a concavity condition Oct 15 revised Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ previous typo were not corrected in title Oct 15 comment Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ @joriki a) You are right. b) I agree. c) I see your point, but I can't find my error. Writing $\hat f_n$ for the $n$-th Fourier coefficient of $f$, I have $\hat f_0=0$ and $\hat f_n=\frac{1}{2 \pi}\int t e^{-int}dt=\frac{1}{2 \pi}\frac{te^{-int}}{(-in)}+0$. Oct 15 revised Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ typos in last per joriki comment Oct 15 revised Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ fourier series vs fourier sum Oct 15 comment Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ @joriki I tried to clarified the notation, and you were right for $0 \le k \le 2n$. Thank you. Sorry for the many typos, Fourier analysis is a jungle for which my machete is not sharp yet. Oct 15 revised Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ edit per joriki comment Oct 15 accepted Inequality for term of a positive sequence : show $\frac{1}{n} \ge c_n - c_{n+1} \ge \frac{1}{n+1}$ Oct 15 comment Show $\left\lvert \frac{1}{\pi+2} \sum_{0 \le k \le 2n,k\ne n} \frac{i}{k-n} e^{ikt} \right\rvert > c \ln n, c>0$ @did The title was inacurrate. Thank you.