Conditions for Functions of Many Complex Variables to be Analytic.?
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From: Robert Israel on 9 Jul 2010 14:18 bacle <here(a)here.com> writes: > Could anyone please tell me the conditions for a function from > C^n to C^m ( C is the complexes) to be analytic.?. I have looked > thru some online sites, and they are too formal; would someone > please just say something like wether we need C-Riemann to be > satisfied by each variable. > > Thanks.: The simplest perhaps is that each component is locally given by a convergent multivariate power series. Using Hartogs's theorem, it's enough to say that each component of your function is analytic in each variable separately. -- Robert Israel israel(a)math.MyUniversitysInitials.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada |