Convolution of sequences - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-23T13:59:46Z http://mathoverflow.net/feeds/question/107980 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107980/convolution-of-sequences Convolution of sequences B-B 2012-09-24T14:16:33Z 2012-09-24T17:51:25Z <p>Let for given real sequences $(a_n)_{n \in \mathbb Z}, (b_n)_{n \in \mathbb Z}$, $c_n:=\sum_{k\in \mathbb Z} a_k b_{n-k}$ for $n \in \mathbb Z$ be the convolution of sequences $(a_n)$, $(b_n)$. </p> <p>For classical convolution if one of two functions is in $L^p$, the second in $L^q$, where $1\leq p,q &lt;\infty$ then their convolution $f*g$ is in $L^r$, where $\frac{1}{r}=\frac{1}{p}+\frac{1}{q}-1$. Is it some similar type theorem true for convolution of sequences?</p> http://mathoverflow.net/questions/107980/convolution-of-sequences/107995#107995 Answer by Gerald Edgar for Convolution of sequences Gerald Edgar 2012-09-24T17:51:25Z 2012-09-24T17:51:25Z <p>Yes. True not only for $\mathbb Z$ but for for abelian (more generally unimodular) locally compact group. (20.18) in Hewitt &amp; Ross, <em>Abstract Harmonic Analysis</em>.</p>