caa a22 4500 445836504 CHVBK 20180317145331.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00209-010-0765-7 doi (NATIONALLICENCE)springer-10.1007/s00209-010-0765-7 Kalmes T. FB 4-Mathematik, Universität Trier, 54286, Trier, Germany aut Every P -convex subset of $${\mathbb{R}^2}$$ is already strongly P -convex [Elektronische Daten] [T. Kalmes] A classical result of Malgrange says that for a polynomial P and an open subset Ω of $${\mathbb{R}^d}$$ the differential operator P(D) is surjective on C ∞(Ω) if and only if Ω is P-convex. Hörmander showed that P(D) is surjective as an operator on $${\fancyscript{D}'(\Omega)}$$ if and only if Ω is strongly P-convex. It is well known that the natural question whether these two notions coincide has to be answered in the negative in general. However, Trèves conjectured that in the case of d=2 P-convexity and strong P-convexity are equivalent. A proof of this conjecture is given in this note. Springer-Verlag, 2010 Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 721-731 0025-5874 269:3-4<721 2011 269 209 https://doi.org/10.1007/s00209-010-0765-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00209-010-0765-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kalmes T. FB 4-Mathematik, Universität Trier, 54286, Trier, Germany aut NATIONALLICENCE 773 0- Mathematische Zeitschrift Springer-Verlag 269/3-4(2011-12-01), 721-731 0025-5874 269:3-4<721 2011 269 209 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer