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The Zorn property for holomorphic functions

Volume 120 / 2017

Thai Thuan Quang, Duong Thanh Vy, Le Thanh Hung, Pham Hien Bang Annales Polonici Mathematici 120 (2017), 115-133 MSC: 32A10, 46A04, 46E50, 46G20, 46A63. DOI: 10.4064/ap170707-11-11 Published online: 4 December 2017

Abstract

The aim of this paper is to investigate Zorn’s property for the space $(E_B, \tau _E)$, where $E_B$ the linear hull of some compact, absolutely convex subset $B$ of a Fréchet space $E$ and the topology $\tau _E$ on $E_B$ is induced by the topology of $E.$ Furthermore, holomorphic extensions from $(E_B, \tau _E)$ are considered. Based on these results, we establish some results on extension of a Fréchet-valued continuous function $f$ to an entire function from a non-polar balanced convex compact subset $B$ of a Fréchet space whenever $f$ is approximated fast enough on $B$ by a sequence of polynomials.

Authors

  • Thai Thuan QuangDepartment of Mathematics
    Quy Nhon University
    170 An Duong Vuong
    Quy Nhon, Binh Dinh, Vietnam
    e-mail
  • Duong Thanh VyDepartment of Mathematics
    Quy Nhon University
    170 An Duong Vuong
    Quy Nhon, Binh Dinh, Vietnam
    e-mail
  • Le Thanh HungDepartment of Mathematics
    Vinh Phuc College
    2 Trung Trac Street
    Phuc Yen, Vinh Phuc, Vietnam
    e-mail
  • Pham Hien BangDepartment of Mathematics
    Thai Nguyen University of Education
    Luong Ngoc Quyen Street
    Thai Nguyen City, Vietnam
    e-mail

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