most recent 30 from http://mathoverflow.net 2013-05-24T21:41:45Z http://mathoverflow.net/feeds/question/92539 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/92539/different-types-of-calculi pbs 2012-03-29T08:22:39Z 2012-03-30T07:32:24Z

<p>We can define a derivation over a field $K$ to be a map $D:K\rightarrow K$ such that </p> <p>$D(u+v) = Du + Dv$ and $D(uv) = uDv + vDu$,</p> <p>for $u,v\in K$, and the constant subfield</p> <p>$Const_D(K) = \lbrace u\in K : Du=0 \rbrace$</p> <p>of $K$ with respect to $D$.</p> <p>From this, we can get the familiar analytic properties of differentiation.</p> <p>My question is: are there any other operators similar to this which we can define over a field, from which we then get some interesting relation to the analytic world.</p> <p>pbs</p>