From: delliott@Glue.umd.edu (David L. Elliott) Newsgroups: sci.math Subject: Re: Doubly Periodic Functions? Date: 15 Sep 1995 18:29:18 -0400 In article <43bknf$cgi@rzsun02.rrz.uni-hamburg.de>, Hauke Reddmann wrote: >Another question: >So f in R has max 1 period >f in C can have 2 periods. >Max 2 periods??? If yes, quaternions -> 4 periods? > You may be right, but remember that the results quoted about periodicity and double periodicity are for _analytic_ (holomorphic) functions. If you consider a larger class of smooth functions f: R^n --> R^n you can have all the periods you want in trivial ways. Elliptic functions are more than just doubly-periodic... Now as to quaternions, the problem is that there are not very many analytic quaternion functions (you can have right analyticity and also left analyticity, since multiplication isn't commutative)... see the work of Fueter in (I think) Comm. Math. Helv. about 1937. David -- David L. Elliott delliott@src.umd.edu Institute for Systems Research/ A.V. Williams Building University of Maryland/ College Park, MD 20742