Interpolation by periods in planar domain [article]

Mikhail Dubashinskiy
2015 arXiv   pre-print
Let Ω⊂ R^2 be a countably connected domain. To any closed differential form of degree 1 in Ω with components in L^2(Ω) one associates the sequence of its periods around holes in Ω, that is around bounded connected components of R^2∖Ω. For which Ω the collection of such period sequences coincides with ℓ^2? We give the answer in terms of metric properties of holes in Ω.
arXiv:1511.07015v1 fatcat:koorfaswknbojjmupzax2couka