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Asymptotic Interpolating Sequences in Uniform Algebras
Author(s) -
Gorkin Pamela,
Mortini Raymond
Publication year - 2003
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610702004039
Subject(s) - mathematics , sequence (biology) , type (biology) , interpolation (computer graphics) , spectrum (functional analysis) , asymptotic expansion , pure mathematics , characterization (materials science) , algebra over a field , combinatorics , discrete mathematics , mathematical analysis , image (mathematics) , physics , computer science , ecology , genetics , quantum mechanics , artificial intelligence , optics , biology
T. Hosokawa, K. Izuchi and D. Zheng recently introduced the concept of asymptotic interpolating sequences (of type 1) in the unit disk for H ∞ (D). It is shown that these sequences coincide with sequences that are interpolating for the algebra QA . Also a characterization is given of the interpolating sequences of type 1 for H ∞ (D), and asymptotic interpolating sequences in the spectrum of H ∞ (D) are studied. The existence of asymptotic interpolating sequences of type 1 for H ∞ (Ω) on arbitrary domains is verified. It is shown that any asymptotic interpolating sequence in a uniform algebra eventually is interpolating.