On uniform convergence for ( μ, ν ) -type rational approximants in ℂ n -II

Clement H. Lutterodt

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-6

Abstract:

This paper shows that if f ( z ) is analytic in some neighborhood of the origin, but meromorphic in ℂ n otherwise, with a denumerable non-accumulating pole sections in ℂ n and if for each fixed ν the pole set of each ( μ , ν ) unisolvent rational approximant π μ ν ( z ) tends to infinity as μ ′ = min i ≤ n ( μ i ) → ∞ , then f ( z ) must be entire in ℂ n . This paper also shows a monotonicity property for the error sequence e μ ν = ‖ f ( z ) − π μ ν ( z ) ‖ K on compact subsets K of ℂ n .

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:357928

DOI: 10.1155/S0161171281000495

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