- -

Algebrability and nowhere Gevrey differentiability

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Algebrability and nowhere Gevrey differentiability

Mostrar el registro completo del ítem

Bastin, F.; Conejero Casares, JA.; Esser, C.; Seoane-Sepulveda, JB. (2015). Algebrability and nowhere Gevrey differentiability. Israel Journal of Mathematics. 205:127-143. https://doi.org/10.1007/s11856-014-1104-1

Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/64755

Ficheros en el ítem

Metadatos del ítem

Título: Algebrability and nowhere Gevrey differentiability
Autor: Bastin, F. Conejero Casares, José Alberto Esser, C. Seoane-Sepulveda, J. B
Entidad UPV: Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Fecha difusión:
Resumen:
We show that there exist c-generated algebras (and dense in C (a)([0, 1])) every nonzero element of which is a nowhere Gevrey differentiable function. This leads to results of dense algebrability (and, therefore, lineability) ...[+]
Palabras clave: Function-spaces , Sets , Spaceability
Derechos de uso: Reserva de todos los derechos
Fuente:
Israel Journal of Mathematics. (issn: 0021-2172 )
DOI: 10.1007/s11856-014-1104-1
Editorial:
Springer Verlag (Germany)
Versión del editor: http://link.springer.com/article/10.1007/s11856-014-1104-1
Código del Proyecto:
info:eu-repo/grantAgreement/MICINN//MTM2010-14909/ES/HIPERCICLICIDAD Y CAOS DE OPERADORES/
info:eu-repo/grantAgreement/UPV//SP20120700/
info:eu-repo/grantAgreement/CNPq// 401735%2F2013-3%2FPVE - Linha 2/
Descripción: "The final publication is available at Springer via http://dx.doi.org/10.1007/s11856-014-1104-1”
Agradecimientos:
The fourth author was supported by CNPq Grant 401735/2013-3 (PVE - Linha 2).
Tipo: Artículo

References

R. M. Aron, F. J. García-Pacheco, D. Pérez-García and J. B. Seoane-Sepúlveda, On dense-lineability of sets of functions on ℝ, Topology 48 (2009), 149–156.

R. M. Aron, V. I. Gurariy and J. B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on ℝ, Proceedings of the American Mathematical Society 133 (2005), 795–803.

R. M. Aron, D. Pérez-García and J. B. Seoane-Sepúlveda, Algebrability of the set of non-convergent Fourier series, Studia Mathematica 175 (2006), 83–90 [+]
R. M. Aron, F. J. García-Pacheco, D. Pérez-García and J. B. Seoane-Sepúlveda, On dense-lineability of sets of functions on ℝ, Topology 48 (2009), 149–156.

R. M. Aron, V. I. Gurariy and J. B. Seoane-Sepúlveda, Lineability and spaceability of sets of functions on ℝ, Proceedings of the American Mathematical Society 133 (2005), 795–803.

R. M. Aron, D. Pérez-García and J. B. Seoane-Sepúlveda, Algebrability of the set of non-convergent Fourier series, Studia Mathematica 175 (2006), 83–90

R. M. Aron and J. B. Seoane-Sepúlveda, Algebrability of the set of everywhere surjective functions on ℂ, Bulletin of the Belgian Mathematical Society. Simon Stevin 14 (2007), 25–31.

M. Balcerzak, A. Bartoszewicz and M. Filipczak, Nonseparable spaceability and strong algebrability of sets of continuous singular functions, Journal of Mathematical Analysis and Applications 407 (2013), 263–269.

A. Bartoszewicz, M. Bienias, M. Filipczak and S. G_lşab, Exponential-like function method in strong c-algebrability, arXiv:1307.0331.

A. Bartoszewicz and S. Głşab, Strong algebrability of sets of sequences and functions, Proceedings of the American Mathematical Society 141 (2013), 827–835.

A. Bartoszewicz and S. Głşab, Additivity and lineability in vector spaces, Linear Algebra and its Applications 439 (2013), 2123–2130.

F. Bastin, C. Esser and S. Nicolay, Prevalence of “nowhere analyticity”, Studia Mathematica 210 (2012), 239–246.

F. Bayart and L. Quarta, Algebras in sets of queer functions, Israel Journal of Mathematics 158 (2007), 285–296.

L. Bernal-González, Lineability of sets of nowhere analytic functions, Journal of Mathematical Analysis and Applications 340 (2008), 1284–1295.

L. Bernal-González, Algebraic genericity of strict-order integrability, Studia Mathematica 199 (2010), 279–293.

L. Bernal-González, D. Pellegrino and J. B. Seoane-Sepúlveda, Linear subsets of nonlinear sets in topological vector spaces, Bulletin of the American Mathematical Society (N.S.) 51 (2014), 71–130, DOI: http://dx.doi.org/ 10.1090/S0273-0979-2013-01421-6 .

G. Botelho, D. Cariello, V. V. Fávaro and D. Pellegrino, Maximal spaceability in sequence spaces, Linear Algebra and its Applications 437 (2012), 2978–2985.

G. Botelho, D. Cariello, V. V. Fávaro, D. Pellegrino and J. B. Seoane-Sepúlveda, Distinguished subspaces of L p of maximal dimension, Studia Mathematica 215 (2013), 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.

S.-Y. Chung and J. Chung, There exist no gaps between Gevrey differentiable and nowhere Gevrey differentiable, Proceedings of the American Mathematical Society 133 (2005), 859–863 (electronic).

J. A. Conejero, P. Jiménez-Rodríguez, G. A. Muñoz-Fernández and J. B. Seoane-Sepúlveda, When the Identity Theorem “seems” to fail, American Mathematical Monthly 121 (2014), 60–68.

P. H. Enflo, V. I. Gurariy and J. B. Seoane-Sepúlveda, Some results and open questions on spaceability in function spaces, Transactions of the American Mathematical Society 366 (2014), 611–625. DOI: http://dx.doi.org/ 10.1090/S0002-9947-2013-05747-9 .

V. P. Fonf, V. I. Gurariy and M. I. Kadets, An infinite-dimensional subspace of C[0, 1]consisting of nowhere differentiable functions, Comptes Rendus de l’Académie Bulgare des Sciences 52 (1999), 13–16.

D. García, B. C. Grecu, M. Maestre and J. B. Seoane-Sepúlveda, Infinite dimensional Banach spaces of functions with nonlinear properties, Mathematische Nachrichten 283 (2010), 712–720.

F. J. García-Pacheco, M. Martín and J. B. Seoane-Sepúlveda, Lineability, spaceability, and algebrability of certain subsets of function spaces, Taiwanese Journal of Mathematics 13 (2009), 1257–1269.

V. I. Gurariy, Subspaces and bases in spaces of continuous functions, Dokladi Akademii Nauk SSSR 167 (1966), 971–973.

V. I. Gurariy and L. Quarta, On lineability of sets of continuous functions, Journal of Mathematical Analysis and Applications 294 (2004), 62–72.

S. Hencl, Isometrical embeddings of separable Banach spaces into the set of nowhere approximatively differentiable and nowhere Hölder functions, Proceedings of the American Mathematical Society 128 (2000), 3505–3511.

B. R. Hunt, T. Sauer and J. A. Yorke, Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces, Bulletin of the American Mathematical Society 27 (1992), 217–238.

B. Levine and D. Milman, 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 (1940), 102–105.

D. Morgenstern, Unendlich oft differenzierbare nicht-analytische Funktionen, Mathematische Nachrichten 12 (1954), 74.

L. Rodríguez-Piazza, Every separable Banach space is isometric to a space of continuous nowhere differentiable functions, Proceedings of the American Mathematical Society 123 (1995), 3649–3654.

R. L. Wheeden and A. Zygmund, Measure and Integral, Pure and Applied Mathematics, Vol. 43, Marcel Dekker, New York, 1977.

T. Yamanaka, A new higher order chain rule and Gevrey class, Annals of Global Analysis and Geometry 7 (1989), 179–203.

[-]

recommendations

 

Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro completo del ítem