Infinite dimensional Banach spaces of functions with nonlinear properties |
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| Authors: | D García B C Grecu M Maestre J B Seoane‐Sepülveda |
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| Institution: | 1. Departamento de An?lisis Matem?tico, Universidad de Valencia, Doctor Moliner 50, 46100 Burjasot Valencia, Spain;2. Department of Pure Mathematics, Queens University Belfast, BT7 1NN, UK;3. Departamento de An?lisis Matem?tico, Facultad de Ciencias Matem?ticas, Universidad Complutense de Madrid, Plaza de las Ciencias 3, 28040 Madrid, Spain |
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| Abstract: | 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 ?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 (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Local extrema Fourier transform Denjoy‐Clarkson property Riemann integrability |
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