Nonlinear Convergence Sets of Divergent Power Series

Details Nonlinear Convergence Sets of Divergent Power Series Nonlinear Convergence Sets of Divergent Power Series

2011-04-10

arxiv.org/abs/1104.1778v5

Mathematics

Complex Variables

5 pages

Scientific paper

A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar-Moh, is introduced. Given a family y=\phi_{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+... of analytic curves in C\timesC^{n} passing through the origin, Conv_{\phi}(f) of a formal power series f(y,t,x)\inC[[y,t,x]] is defined to be the set of all s\inC for which the power series f(\phi_{s}(t,x),t,x) converges as a series in (t,x). We prove that for a subset E\subsetC there exists a divergent formal power series f(y,t,x)\inC[[y,t,x]] such that E=Conv_{\phi}(f) if and only if E is a F_{{\sigma}} set of zero capacity. This generalizes the results of P. Lelong and A. Sathaye for the linear case \phi_{s}(t,x)=st.

Affiliated with

Also associated with

No associations

Rating

Nonlinear Convergence Sets of Divergent Power Series does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonlinear Convergence Sets of Divergent Power Series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear Convergence Sets of Divergent Power Series will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-316442