Infinite dimensional Banach spaces of functions with nonlinear properties
| dc.contributor.author | García, D. | |
| dc.contributor.author | Grecu, B.C. | |
| dc.contributor.author | Maestre, Manuel | |
| dc.contributor.author | Seoane Sepúlveda, Juan Benigno | |
| dc.date.accessioned | 2023-06-20T03:30:54Z | |
| dc.date.available | 2023-06-20T03:30:54Z | |
| dc.date.issued | 2010 | |
| dc.description.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 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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC and FEDER | |
| dc.description.sponsorship | Marie Curie Intra European Fellowship | |
| dc.description.sponsorship | MEC and FEDER | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/20031 | |
| dc.identifier.doi | 10.1002/mana.200610833 | |
| dc.identifier.issn | 0025-584X | |
| dc.identifier.officialurl | http://onlinelibrary.wiley.com/doi/10.1002/mana.200610833/pdf | |
| dc.identifier.relatedurl | http://www.wiley.com | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43664 | |
| dc.issue.number | 5 | |
| dc.journal.title | Mathematische Nachrichten | |
| dc.language.iso | eng | |
| dc.page.final | 720 | |
| dc.page.initial | 712 | |
| dc.publisher | Wiley-Blackwell | |
| dc.relation.projectID | MTM2005-08210 | |
| dc.relation.projectID | MEIF-CT-2005-006958 | |
| dc.relation.projectID | MTM2005-08210. | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.98 | |
| dc.subject.keyword | Local extrema | |
| dc.subject.keyword | Fourier transform | |
| dc.subject.keyword | Denjoy-Clarkson property | |
| dc.subject.keyword | Riemann integrability | |
| dc.subject.ucm | Análisis funcional y teoría de operadores | |
| dc.title | Infinite dimensional Banach spaces of functions with nonlinear properties | |
| dc.type | journal article | |
| dc.volume.number | 283 | |
| dcterms.references | R. M. Aron, C. Boyd, R. Ryan, and I. Zalduendo, Zeros of polynomials on Banach spaces: the real story, Positivity 7,No. 4, 285–295 (2003). R. M. Aron, D. Garcıa, and M. Maestre, Linearity in non-linear problems, RACSAM Rev. R. Acad. Cienc. Exactas Fıs.Nat. Ser. A Mat. 95, No. 1, 7–12 (2001). R. M. Aron, V. I. Gurariy, and J. B. Seoane-Sepulveda,Lineability and spaceability of sets of functions on R, Proc.Amer. Math. Soc. 133, 795–803 (2005). R. M. Aron and P.Hajek, Zero sets of polynomials in several variables, Arch. Math. (Basel) 86, No. 6, 561–568 (2006). R. M. Aron, D. Perez-Garcia, and J. B. Seoane-Sepulveda,Algebrability of the set of non-convergent Fourier series,Studia Math. 175, 83–90 (2006). H. J. M. Bos, R. Bunn, J. W. Dauben, I. Grattan-Guinness,T. W. Hawkins, and K. M. Pedersen, From the calculus to set theory, in: An Introductory History, edited by I. Grattan-Guinness (Gerald Duckworth & Co. Ltd., London, 1980),pp. 1630–1910. Z. Buczolich, Solution to the gradient problem of C. E.Weil, Rev. Mat. Iberoamericana 21, No. 3, 889–910 (2005). J. A. Clarkson and P. Erdos, Approximation by polynomials,Duke Math. J. 10, 5–11 (1943). R. Deville and E. Matheron, Infinite games, Banach space geometry and the eikonal equation, Proc. Lond. Math. Soc.(3) 95, No. 1, 49–68 (2007). V. Drobot and M. Morayne, Continuous functions with a dense set of proper local maxima, Amer. Math. Monthly 92,No. 3, 209–211 (1985). P. Enflo and V. I. Gurariy, On lineability and spaceability of sets in function spaces, preprint (2000). J. Ferrer, An approximate Rolle’s theorem for polynomials of degree four in a Hilbert space, Publ. Res. Inst. Math.Sci.41, No. 2, 375–384 (2005). V. I. Gurariy, Subspaces and bases in spaces of continuous functions, Dokl. Akad. Nauk SSSR 167, 971–973 (1966) (in Russian). B. R. Gelbaum and J. M. H. Olmsted, Counterexamples in Analysis (Dover Publications, New York, 2003). F. J. Garcıa-Pacheco, N. Palmberg, and J. B. Seoane-Sepulveda, Lineability and algebrability of pathological phenomena in analysis, J. Math. Annal. Appl. 326, No. 2,929–939 (2007). H. Lebesgue, Lec¸ons sur l’Integration (Gauthier-Villars,Paris, 1904). J. Maly, The Darboux property for gradients, Real Anal. Exchange 22, No. 1, 167–173 (1996/97). E. E. Posey and J. E. Vaughan,Functions with a proper local maximum in each interval,Amer. Math.Monthly 90,No.4, 281–282(1983). C. E. Weil, On properties of derivatives, Trans. Amer.Math. Soc. 114, 363–376 (1965). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | e85d6b14-0191-4b04-b29b-9589f34ba898 | |
| relation.isAuthorOfPublication.latestForDiscovery | e85d6b14-0191-4b04-b29b-9589f34ba898 |
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