Convergence in capacity of rational approximants of meromorphic functions | Zendy

Hans-Peter Blatt | Zendy

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Convergence in capacity of rational approximants of meromorphic functions

Author(s) -

Hans-Peter Blatt

Publication year - 2014

Publication title -

publications de l institut mathematique

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.246

H-Index - 17

eISSN - 1820-7405

pISSN - 0350-1302

DOI - 10.2298/pim1410031b

Subject(s) - meromorphic function , subsequence , mathematics , degree (music) , convergence (economics) , rate of convergence , domain (mathematical analysis) , rational function , mathematical analysis , pure mathematics , combinatorics , physics , economics , computer science , computer network , channel (broadcasting) , acoustics , bounded function , economic growth

Let f be meromorphic on the compact set EC with maximal Green domain of meromorphy E(f ), (f) < 1. We investigate rational ap- proximants with numerator degree 6 n and denominator degree 6 mn for f. We show that the geometric convergence rate on E implies convergence in ca- pacity outside E if mn = o(n) as n ! 1. Further, we show that the condition is sharp and that the convergence in capacity is uniform for a subsequence Λ N.

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