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Infinite dimensional Banach spaces of functions with nonlinear properties



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García, D. and Grecu, B.C. and Maestre, Manuel and Seoane-Sepúlveda, Juan B. (2010) Infinite dimensional Banach spaces of functions with nonlinear properties. Mathematische Nachrichten, 283 (5). pp. 712-720. ISSN 0025-584X

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/mana.200610833/pdf



The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on R(n) failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

Item Type:Article
Uncontrolled Keywords:Local extrema, Fourier transform, Denjoy-Clarkson property, Riemann integrability
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:20031
Deposited On:21 Feb 2013 15:22
Last Modified:25 Nov 2016 12:41

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