VSE knjižnice (vzajemna bibliografsko-kataložna baza podatkov COBIB.SI)
  • Small families of complex lines for testing holomorphic extendibility
    Globevnik, Josip, 1945-
    Let $B$ be the open unit ball in ▫${\Bbb C}^2$▫. This paper deals with the analog of Hartogs' separate analyticity theorem for CR functions on the sphere ▫$bB$▫. We prove such a theorem for functions ... in ▫$C^\infty (bB)$▫: If ▫$a, b \in \overline B$▫, ▫$a \ne b$▫ and if ▫$f \in C^\infty (bB)$▫ extends holomorphically into ▫$B$▫ along any complex line passing through either ▫$a$▫ or ▫$b$▫, then ▫$f$▫ extends holomorphically through ▫$B$▫. On the other hand, for each ▫$k \in \Bbb{N}$▫ there is a function ▫$f \in C^k(bB)$▫ which extends holomorphically into ▫$B$▫ along any complex line passing through either ▫$a$▫ or ▫$b$▫ yet ▫$f$▫ does not extend holomorphically through ▫$B$▫. More generally, in the paper we obtain a fairly complete description of pairs of points ▫$a, b \in {\Bbb C}^2$, $a \ne b$▫, such that if ▫$f \in C^\infty (bB)$▫ extends holomorphically into ▫$B$▫ along every complex line passing through either ▫$a$▫ or ▫$b$▫ that meets ▫$B$▫, then ▫$f$▫ extends holomorphically through ▫$B$▫.
    Vir: American journal of mathematics. - ISSN 0002-9327 (Vol. 134, no. 6, 2012, str. 1473-1490)
    Vrsta gradiva - članek, sestavni del
    Leto - 2012
    Jezik - angleški
    COBISS.SI-ID - 16521561

    Povezava(-e):

    http://dx.doi.org/10.1353/ajm.2012.0045

vir: American journal of mathematics. - ISSN 0002-9327 (Vol. 134, no. 6, 2012, str. 1473-1490)
loading ...
loading ...
loading ...

Vnos na polico