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2019 Strong algebrability and residuality on certain sets of analytic functions
M.L. Lourenço, D.M. Vieira
Rocky Mountain J. Math. 49(6): 1961-1972 (2019). DOI: 10.1216/RMJ-2019-49-6-1961

Abstract

We show that the set of analytic functions from $\mathbb C^2$ into $\mathbb C^2$, which are not Lorch-analytic is spaceable and strongly $\mathfrak {c}$-algebrable, but is not residual in the space of entire functions from $\mathbb C^2$ into $\mathbb C^2$. We also show that the set of functions which belongs to the disk algebra but not a Dales-Davie algebra is strongly $\mathfrak {c}$-algebrable and is residual in the disk algebra.

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M.L. Lourenço. D.M. Vieira. "Strong algebrability and residuality on certain sets of analytic functions." Rocky Mountain J. Math. 49 (6) 1961 - 1972, 2019. https://doi.org/10.1216/RMJ-2019-49-6-1961

Information

Published: 2019
First available in Project Euclid: 3 November 2019

zbMATH: 07136588
MathSciNet: MR4027243
Digital Object Identifier: 10.1216/RMJ-2019-49-6-1961

Subjects:
Primary: 46G20., ‎46J15
Secondary: 46J10, 46T25

Rights: Copyright © 2019 Rocky Mountain Mathematics Consortium

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Vol.49 • No. 6 • 2019
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