Publication: Lineability, spaceability, and latticeability of subsets of C([0, 1]) and Sobolev spaces
Loading...
Official URL
Full text at PDC
Publication Date
2022-05-21
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer
Abstract
This work is a contribution to the ongoing search for algebraic structures within a nonlinear setting. Here, we shall focus on the study of lineability of subsets of continuous functions on the one hand and within the setting of Sobolev spaces on the other (which represents a novelty in the area of research).
Description
CRUE-CSIC (Acuerdos Transformativos 2022)
UCM subjects
Unesco subjects
Keywords
Citation
1. Aron, R.M., Gurariy, V.I., Seoane-Sepúlveda, J.B.: Lineability and spaceability of sets of functions on R.
Proc. Am. Math. Soc. 133(3), 795–803 (2005). https://doi.org/10.1090/S0002-9939-04-07533-1
2. Aron, R.M., García-Pacheco, F.J., Pérez-García, D., Seoane-Sepúlveda, J.B.: On dense-lineability of sets
of functions on R. Topology 48(2–4), 149–156 (2009). https://doi.org/10.1016/j.top.2009.11.013
3. Aron, R.M., Bernal González, L., Pellegrino, D.M., Seoane-Sepúlveda, J.B.: Lineability: The Search for
Linearity in Mathematics, Monographs and Research Notes in Mathematics. CRC Press, Boca Raton (2016)
4. Bernal-González, L., Pellegrino, D., Seoane-Sepúlveda, J.B.: Linear subsets of nonlinear sets in topological vector spaces. Bull. Am. Math. Soc. (N.S.) 51(1), 71–130 (2014). https://doi.org/10.1090/S0273-0979-2013-01421-6
5. Bernal-González, L., Fernández-Sánchez, J., Seoane-Sepúlveda, J.B., Trutschnig, W.: tHighly tempering infinite matrices II: from divergence to convergence via Toeplitz-Silverman matrices. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(4), Paper No. 202, 10 (2020). https://doi.org/10.1007/s13398-020-00934-z
6. Bonilla, A., Muñoz-Fernández, G.A., Prado-Bassas, J.A., Seoane-Sepúlveda, J.B.: Hausdorff and Box dimensions of continuous functions and lineability. Linear Multilinear Algebra 69(4), 593–606 (2021).
https://doi.org/10.1080/03081087.2019.1612832
7. Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Universitext, Springer,
New York (2011)
8. Ciesielski, K.C., Natkaniec, T.: Different notions of Sierpinski–Zygmund functions. Rev. Mat. Complut. 34(1), 151–173 (2021). https://doi.org/10.1007/s13163-020-00348-w
9. Ciesielski, K.C., Seoane-Sepúlveda, J.B.: A century of Sierpinski–Zygmund functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3863–3901 (2019). https://doi.org/10.1007/s13398-019-00726-0
10. Ciesielski, K.C., Seoane-Sepúlveda, J.B.: Differentiability versus continuity: restriction and extension theorems and monstrous examples. Bull. Am. Math. Soc. (N.S.) 56(2), 211–260 (2019). https://doi.org/ 10.1090/bull/1635
11. Ciesielski, K.C., Gámez-Merino, J.L., Mazza, L., Seoane-Sepúlveda, J.B.: Cardinal coefficients related to surjectivity, Darboux, and Sierpi ´nski–Zygmund maps. Proc. Am. Math. Soc. 145(3), 1041–1052 (2017).
https://doi.org/10.1090/proc/13294
12. Conejero, J.A., Fenoy, M., Murillo-Arcila, M., Seoane-Sepúlveda, J.B.: Lineability within probability theory settings. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 111(3), 673–684 (2017). https://doi.org/10.1007/s13398-016-0318-y
13. de Amo, E., Díaz Carrillo, M., Fernández-Sánchez, J.: Singular functions with applications to fractal dimensions and generalized Takagi functions. Acta Appl. Math. 119, 129–148 (2012). https://doi.org/10.1007/s10440-011-9665-z
14. Dovgoshey, O., Martio, O., Ryazanov, V., Vuorinen, M.: The Cantor function. Expo. Math. 24(1), 1–37 (2006). https://doi.org/10.1016/j.exmath.2005.05.002
15. Falcó, J., Grosse-Erdmann, K.-G.: Algebrability of the set of hypercyclic vectors for backward shift operators. Adv. Math. 366, 107082 (2020). https://doi.org/10.1016/j.aim.2020.107082
16. Falconer, K.: Fractal Geometry. Mathematical Foundations and Applications, 3rd edn. Wiley, Chichester (2014)
17. Fernández Sánchez, J., Trutschnig, W.: A note on singularity of a recently introduced family of Minkowski’s question-mark functions. C. R. Math. Acad. Sci. Paris 355(9), 956–959 (2017). https://doi.org/10.1016/j.crma.2017.09.009 (English, with English and French summaries)
18. Fernández-Sánchez, J., Rodríguez-Vidanes, D.L., Seoane-Sepúlveda, J.B., Trutschnig, W.: Lineability, differentiable functions and special derivatives, Banach J. Math. Anal. 15(1), Paper No. 18, 22 (2021). https://doi.org/10.1007/s43037-020-00103-9
19. García, D., Grecu, B.C., Maestre, M., Seoane-Sepúlveda, J.B.: Infinite dimensional Banach spaces of functions with nonlinear properties. Math. Nachr. 283(5), 712–720 (2010). https://doi.org/10.1002/mana.200610833
20. Jiménez-Rodríguez, P.: c0 is isometrically isomorphic to a subspace of Cantor–Lebesgue functions. J. Math. Anal. Appl. 407(2), 567–570 (2013). https://doi.org/10.1016/j.jmaa.2013.05.033
21. Kunze, H., La Torre, D., Mendivil, F., Vrscay, E.R.: Fractal-Based Methods in Analysis. Springer, New York (2012)
22. Oikhberg, T.: A note on latticeability and algebrability. J. Math. Anal. Appl. 434(1), 523–537 (2016).
https://doi.org/10.1016/j.jmaa.2015.09.025
23. Schwartz, L.: Théorie des distributions, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. IX–X. Nouvelle édition, entiérement corrigée, refondue et augmentée, Hermann, Paris (1966) (French)
24. Seoane-Sepúlveda, J.B.: Chaos and lineability of pathological phenomena in analysis, ProQuest LLC, Ann Arbor (2006). Thesis (Ph.D.), Kent State University
25. Shidfar, A., Sabetfakhri, K.: Notes: on the continuity of Van Der Waerden’s function in the holder sense. Am. Math. Mon. 93(5), 375–376 (1986). https://doi.org/10.2307/2323599
26. Trutschnig, W., Fernández Sánchez, J.: Copulas with continuous, strictly increasing singular conditional
distribution functions. J. Math. Anal. Appl. 410(2), 1014–1027 (2014). https://doi.org/10.1016/j.jmaa.2013.09.032