From: Jan-Christoph Puchta <jcp@arcade.mathematik.uni-freiburg.de>
Subject: Re: functions which are "almost" periodical
Date: Wed, 31 Mar 1999 12:31:08 +0100
Newsgroups: sci.math
To: Main Night <mainnight@aol.com>

Main Night wrote:
> 
> has any work been done on functions which are "almost" periodical, such as
>            sin x if x<>537068275492454098643205.222
> f(x) = {
> 
>            sin x + 0.0000001 if x=537068275492454098643205.222
> ?
>

The usuall approach is to fix some space of functions, define a norm or
seminorm on it and define the subspace of almost periodical functions to
be the closure of the subspace generated by periodic functions. See e.g.
Schwartz & Spilker "Arithmetical Functions" for functions N -> C, or
Maak for a more general approach.


Jan-Christoph Puchta