VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Reflexivity of the space of transversal distributions
    Kališnik, Jure, matematik
    For any smooth, Hausdorff and second-countable manifold ▫$N$▫ one can define the Fréchet space ▫${\mathcal C}^{\infty}(N)$▫ of smooth functions on ▫$N$▫ and its strong dual ▫${\cal E}'(N)$▫ of ... compactly supported distributions on ▫$N$▫. It is a standard result that the strong dual of ▫${\cal E}'(N)$▫ is naturally isomorphic to ▫${\mathcal C}^{\infty}(N)$▫, which implies that both ▫${\mathcal C}^{\infty}(N)$▫ and ▫${\cal E}'(N)$▫ are reflexive locally convex spaces. In this paper we generalise that result to the setting of transversal distributions on the total space of a surjective submersion ▫$\pi : P\to M$▫.We show that the strong ▫${\mathcal C}^{\infty}_c(M)$▫-dual of the space ▫${\cal E}'_{\pi} (P)$▫ of ▫$\pi$▫-transversal distributions is naturally isomorphic to the ▫${\mathcal C}^{\infty}_c(M)$▫-module ▫${\mathcal C}^{\infty}(P)$▫.
    Vir: The Journal of geometric analysis. - ISSN 1050-6926 (Vol. 33, iss. 10, [article no.] 331, Oct. 2023, 20 str.)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2023
    Jezik - angleški
    COBISS.SI-ID - 178959107

    Povezava(-e):

    https://link.springer.com/article/10.1007/s12220-023-01390-y
    DiRROS - Digitalni repozitorij raziskovalnih organizacij Slovenije
    Repozitorij Univerze v Ljubljani – RUL
    DOI

vir: The Journal of geometric analysis. - ISSN 1050-6926 (Vol. 33, iss. 10, [article no.] 331, Oct. 2023, 20 str.)
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