Finite interpolation with minimum uniform norm in C^n

Details Finite interpolation with minimum uniform norm in C^n Finite interpolation with minimum uniform norm in C^n

1997-12-04

arxiv.org/abs/math/9712245v1

Mathematics

Complex Variables

Scientific paper

Given a finite sequence $a:={a_1, ..., a_N}$ in a domain $\Omega \subset C^n$, and complex scalars $v:={v_1, ..., v_N}$, consider the classical extremal problem of finding the smallest uniform norm of a holomorphic function verifying $f(a_j)=v_j$ for all $j$. We show that the modulus of the solutions to this problem must approach its least upper bound along a subset of the boundary of the domain large enough to contain the support of a measure whose hull contains a subset of the original $a$ large enough to force the same minimum norm. Furthermore, all the solutions must agree on a variety which also contains this hull. An example is given to show that the inclusions can be strict.

Affiliated with

Also associated with

No associations

Rating

Finite interpolation with minimum uniform norm in C^n 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 Finite interpolation with minimum uniform norm in C^n, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Finite interpolation with minimum uniform norm in C^n will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-221212