Algebrability and nowhere Gevrey differentiability
Loading...
Full text at PDC
Publication date
2015
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Hebrew University Magnes Press
Citations
Exportar
Citation
Aron, R. M., García-Pacheco, F. J., Pérez-García, D., Seoane-Sepúlveda, J. B. (2009) On dense-lineability of sets of functions on ℝ. Topology 48: pp. 149-156
Aron, R. M., Gurariy, V. I., Seoane-Sepúlveda, J. B. (2005) Lineability and spaceability of sets of functions on ℝ. Proceedings of the American Mathematical Society 133: pp. 795-803
Aron, R. M., Pérez-García, D., Seoane-Sepúlveda, J. B. (2006) Algebrability of the set of non-convergent Fourier series. Studia Mathematica 175: pp. 83-90
Aron, R. M., Seoane-Sepúlveda, J. B. (2007) Algebrability of the set of everywhere surjective functions on ℂ. Bulletin of the Belgian Mathematical Society. Simon Stevin 14: pp. 25-31
Balcerzak, M., Bartoszewicz, A., Filipczak, M. (2013) Nonseparable spaceability and strong algebrability of sets of continuous singular functions. Journal of Mathematical Analysis and Applications 407: pp. 263-269
A. Bartoszewicz, M. Bienias, M. Filipczak and S. G_lşab, Exponential-like function method in strong c-algebrability, arXiv:1307.0331.
Bartoszewicz, A., Głşab, S. (2013) Strong algebrability of sets of sequences and functions. Proceedings of the American Mathematical Society 141: pp. 827-835
Bartoszewicz, A., Głşab, S. (2013) Additivity and lineability in vector spaces. Linear Algebra and its Applications 439: pp. 2123-2130
Bastin, F., Esser, C., Nicolay, S. (2012) Prevalence of “nowhere analyticity”. Studia Mathematica 210: pp. 239-246
Bayart, F., Quarta, L. (2007) Algebras in sets of queer functions. Israel Journal of Mathematics 158: pp. 285-296
Bernal-González, L. (2008) Lineability of sets of nowhere analytic functions. Journal of Mathematical Analysis and Applications 340: pp. 1284-1295
Bernal-González, L. (2010) Algebraic genericity of strict-order integrability. Studia Mathematica 199: pp. 279-293
Bernal-González, L., Pellegrino, D., Seoane-Sepúlveda, J. B. (2014) Linear subsets of nonlinear sets in topological vector spaces. Bulletin of the American Mathematical Society (N.S.) 51: pp. 71-130
Botelho, G., Cariello, D., Fávaro, V. V., Pellegrino, D. (2012) Maximal spaceability in sequence spaces. Linear Algebra and its Applications 437: pp. 2978-2985
Botelho, G., Cariello, D., Fávaro, V. V., Pellegrino, D., Seoane-Sepúlveda, J. B. (2013) Distinguished subspaces of L p of maximal dimension. Studia Mathematica 215: pp. 261-280
G. Botelho, D. Cariello, V. V. Fávaro, D. Pellegrino and J. B. Seoane-Sepúlveda, On very non-linear subsets of continuous functions, Quarterly Journal of Mathematics (2013), in press. doi:10.1093/qmath/hat043.
Chung, S.-Y., Chung, J. (2005) There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable. Proceedings of the American Mathematical Society 133: pp. 859-863
Conejero, J. A., Jiménez-Rodríguez, P., Muñoz-Fernández, G. A., Seoane-Sepúlveda, J. B. (2014) When the Identity Theorem “seems” to fail. American Mathematical Monthly 121: pp. 60-68
Enflo, P. H., Gurariy, V. I., Seoane-Sepúlveda, J. B. (2014) Some results and open questions on spaceability in function spaces. Transactions of the American Mathematical Society 366: pp. 611-625
Fonf, V. P., Gurariy, V. I., Kadets, M. I. (1999) An infinite-dimensional subspace of C[0, 1]consisting of nowhere differentiable functions. Comptes Rendus de l’Académie Bulgare des Sciences 52: pp. 13-16
García, D., Grecu, B. C., Maestre, M., Seoane-Sepúlveda, J. B. (2010) Infinite dimensional Banach spaces of functions with nonlinear properties. Mathematische Nachrichten 283: pp. 712-720
García-Pacheco, F. J., Martín, M., Seoane-Sepúlveda, J. B. (2009) Lineability, spaceability, and algebrability of certain subsets of function spaces. Taiwanese Journal of Mathematics 13: pp. 1257-1269
Gurariy, V. I. (1966) Subspaces and bases in spaces of continuous functions. Dokladi Akademii Nauk SSSR 167: pp. 971-973
Gurariy, V. I., Quarta, L. (2004) On lineability of sets of continuous functions. Journal of Mathematical Analysis and Applications 294: pp. 62-72
Hencl, S. (2000) Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions. Proceedings of the American Mathematical Society 128: pp. 3505-3511
Hunt, B. R., Sauer, T., Yorke, J. A. (1992) Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces. Bulletin of the American Mathematical Society 27: pp. 217-238
Levine, B., Milman, D. (1940) On linear sets in space C consisting of functions of bounded variation. Comm. Inst. Sci. Math. Méc. Univ. Kharkoff [Zapiski Inst. Mat. Mech.] (4) 16: pp. 102-105
Morgenstern, D. (1954) Unendlich oft differenzierbare nicht-analytische Funktionen. Mathematische Nachrichten 12: pp. 74
Rodríguez-Piazza, L. (1995) Every separable Banach space is isometric to a space of continuous nowhere differentiable functions. Proceedings of the American Mathematical Society 123: pp. 3649-3654
Wheeden, R. L., Zygmund, A. (1977) Measure and Integral. Marcel Dekker, New York
Yamanaka, T. (1989) A new higher order chain rule and Gevrey class. Annals of Global Analysis and Geometry 7: pp. 179-203
Abstract
We show that there exist c-generated algebras (and dense in C ∞([0, 1])) every nonzero element of which is a nowhere Gevrey differentiable function. This leads to results of dense algebrability (and, therefore, lineability) of functions enjoying this property. In the process of proving these results we also provide a new construction of nowhere Gevrey differentiable functions.