Journal
MATHEMATISCHE NACHRICHTEN
Volume 283, Issue 5, Pages 712-720Publisher
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.200610833
Keywords
Local extrema; Fourier transform; Denjoy-Clarkson property; Riemann integrability
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Funding
- MEC
- FEDER [MTM2005-08210]
- Marie Curie Intra European Fellowship [MEIF-CT-2005-006958]
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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. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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