Hopeless Fourier transform? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T17:56:36Z http://mathoverflow.net/feeds/question/100774 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/100774/hopeless-fourier-transform Hopeless Fourier transform? Alex A 2012-06-27T13:03:37Z 2012-06-27T13:03:37Z <p>Let $Y_2(x)$ denote the Bessel function of second kind and second order. I'm interested in the Fourier transform of the reciprocal $1/Y_2(|x|)$ in the distributional sense. I suppose there is not much hope of a closed formula for the transform, but all I need is that the Fourier transform of $1/Y_2(|x|)$ is real analytic away from $\pm 1$ but not real analytic in any neighborhood of $\pm 1$. </p> <p>What kind of methods/theorems could one use to analyze this question? </p>