On the rapidly convergence in capacity of the sequence of holomorphic functions | Zendy

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On the rapidly convergence in capacity of the sequence of holomorphic functions

Author(s) -

Kieu Chi

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1909627c

Subject(s) - mathematics , holomorphic function , sequence (biology) , bounded function , domain (mathematical analysis) , boundary (topology) , convergence (economics) , constant (computer programming) , combinatorics , discrete mathematics , pure mathematics , mathematical analysis , genetics , computer science , economics , biology , programming language , economic growth

In this paper, we are interested in finding sufficient conditions on a Borel set X lying either inside a bounded domain D ? Cn or in the boundary ?D so that if {rm}m?1 is a sequence of rational functions and {fm}m?1 is a sequence of bounded holomorphic functions on D with {fm-rm}m?1 is convergent fast enough to 0 in some sense on X then the convergence occurs on the whole domain D. The main result is strongly inspired by Theorem 3.6 in [3] whether the f fmg is a constant sequence.

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