Institutos Universitarios

  1. Portada
  2. Programmes
  3. 2020-present
  4. Interactions of Functional Analysis with Algebra, Geometry and Topology

Interactions of Functional Analysis with Algebra, Geometry and Topology

Brief description

This program falls within several interdisciplinary fields within Pure Mathematics. More precisely,

  • Certain linear, non-linear, and geometric aspects of Analysis (such as Geometric Analysis, Differentiability, Geometry of Banach spaces, Lineability and Spaceability, and classical inequalities).
  • Banach Spaces and Lattices, and operators between them. General Operator theory, Chaotic and Hypercyclic Operators.
  • The study of General Topology and Group Theory (Lie groups, semisimple groups, compact groups, Topological abelian groups, among others) via many different techniques from many other areas in Mathematics (such as, for instance, techniques inherited from Functional Analysis).

 

Researchers

 

Publications

  • S. Dantas, D. García, M. Maestre, J. B. Seoane-Sepúlveda. The Daugavet Equation: Linear and Nonlinear Recent Results. In Mathematics Online First Collections. Springer, 2023, 1-53. https://doi.org/10.1007/16618_2023_60
  • J. Fernández-Sánchez, S. Maghsoudi, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. The Set of p-Adic Continuous Functions not Satisfying the Luzin (N) Property. Results in Mathematics. 2023, 78, Article number 157. https://doi.org/10.1007/s00025-023-01933-3
  • J. Fernández Sánchez, J. López-Salazar Codes, J. B. Seoane Sepúlveda, W. Trutschnig. Generalized Notions of Continued Fractions. Ergodicity and Number Theoretic Applications, CRC Press, 2023. ISBN: 978-1-032-51678-3

  • P.H Enflo, M.S. Moslehian, J.B. Seoane-Sepúlveda, A history of solving some famous problems in mathematical analysis. British Journal for the History of Mathematics, 2022, 37(1), 64-80. https://doi.org/10.1080/26375451.2022.2037358
  •  R. Campoamor-Stursberg. On some algebraic formulations within universal enveloping algebras related to superintegrability, Acta Polytechnica, 2022, 62(1), 16–22, https://doi.org/10.14311/AP.2022.62.0016
  • J. Fernández-Sánchez. J. B. Seoane-Sepúlveda. W. Trutschnig. Lineability, algebrability, and sequences of random variables. Mathematische Nachrichten. 2022. http://doi.org/10.1002/mana.202000102
  • J. Fernández-Sánchez, S. Maghsoudi, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Classical vs. non-Archimedean analysis: an approach via algebraic genericity. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2022, 116, 2, Article number 72. https://doi.org/10.1007/s13398-022-01209-5
  • T. Borsich, X. Domínguez, E. Martín-Peinador. On the existence of topologies compatible with a group duality with predetermined properties. Topology and its Applications. 2022, Article number 107964. https://doi.org/10.1016/j.topol.2021.107964
  • R. Campoamor-Stursberg, I. Marquette. Quadratic algebras as commutants of algebraic Hamiltonians in the enveloping algebra of Schrödinger algebras. Annals of Physics. 2022, 437, Article number 168694. https://doi.org/10.1016/j.aop.2021.168694
  • R. Campoamor-Stursberg. Lie-symmetry analysis of the Painlevé-Gambier classification of second-order scalar ordinary differential equations. In Advances in Mathematics Research. 2021, 29, 77 - 131. ISBN: 978-1-53619-759-4. Link.
  • J. Khodabandehlo, S. Maghsoudi, J. B. Seoane-Sepúlveda. Lineability, continuity and antiderivatives in the non-Archimedean setting. Canadian Mathematical Bulletin. 2021, 64, 3, 638-650. https://doi.org/10.4153/S0008439520000715
  • M. Fenoy, G. A. Muñoz-Fernández, J. R. Pareja Monturiol, J. B. Seoane-Sepúlveda. Healthy versus congestive heart failure patients — An approach via the Hurst parameter. Communications in Nonlinear Science and Numerical Simulation. 2021, 103, Article number 106004. https://doi.org/10.1016/j.cnsns.2021.106004
  • Jiménez-Rodríguez, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes. Geometry of spaces of homogeneous trinomials on R2. Banach Journal of Mathematical Analysis. 2021, 15, 4, Article number 61. https://doi.org/10.1007/s43037-021-00144-8
  • L. Bernal-González, J. Fernández-Sánchez, M. E. Martínez-Gómez, J. B. Seoane-Sepúlveda. Banach spaces and Banach lattices of singular functions. Studia Mathematica. 2021, 260, 2, 167–194. https://doi.org/10.4064/sm200419-7-9
  • R. Campoamor-Stursberg. On some structural properties of semidirect sums of so(3) and Abelian lie algebras. Geometry, Integrability and Quantization. 2021, 22, 88 - 106. https://doi.org/10.7546/giq-22-2021-88-106
  • J. Khodabandehlou, S. Maghsoudi, J. B. Seoane-Sepúlveda. Algebraic genericity and summability within the non-Archimedean setting. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 2021, 115, 21. https://link.springer.com/article/10.1007/s13398-020-00961-w
  • J. A. Adell, J. Falcó, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Discontinuous, although “highly” differentiable, real functions and algebraic genericity. Journal of Mathematical Analysis and Applications. 2021, 502, 2, 125264. https://doi.org/10.1016/j.jmaa.2021.125264
  • P. Jiménez-Rodríguez, M. E. Martínez-Gómez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. Injectiveness and discontinuity of multiplicative convex functions. Mathematics. 2021, 9(9), Article number 1035. https://doi.org/10.3390/math9091035
  • A. Ballesteros, R. Campoamor-Stursberg, E. Fernández-Saiz, F. J. Herranz, J. De Lucas. Poisson-Hopf deformations of Lie-Hamilton systems revisited: Deformed superposition rules and applications to the oscillator algebra. Journal of Physics A: Mathematical and Theoretical. 2021, 54, 20, Article number abf1db. https://doi.org/10.1088/1751-8121/abf1db
  • R. Deville, M. Jiménez-Sevilla. Normal and starlike tilings in separable Banach spaces. Journal of Mathematical Analysis and Applications. 2021, 500, 2, Article number 125116. https://doi.org/10.1016/j.jmaa.2021.125116
  • R. Campoamor-Stursberg, I. Marquette. Hidden symmetry algebra and construction of quadratic algebras of superintegrable systems. Annals of Physics. 2021, 424, 168378. https://doi.org/10.1016/j.aop.2020.168378
  • M. C. Nucci, R. Campoamor-Stursberg. Maximally superintegrable systems in flat three-dimensional space are linearizable. Journal of Mathematical Physics. 2021, 62, 1, 1, Article number 0007377. https://doi.org/10.1063/5.0007377
  • A. Bonilla, G. A. Muñoz-Fernández, J. A. Prado-Bassas, J. B. Seoane-Sepúlveda. Hausdorff and Box dimensions of continuous functions and lineability. Linear and Multilinear Algebra. Published online: 06 May 2019 https://doi.org/10.1080/03081087.2019.1612832
  • I. Caamaño, J. A. Jaramillo, A. Prieto, A. Ruiz de Alarcón. Sobolev spaces of vector-valued functions. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2021, 115 (1), art. no. 19. https://doi.org/10.1007/s13398-020-00959-4
  • L. Bernal-González, H. J. Cabana, D. García, M. Maestre, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. A new approach towards estimating the n-dimensional Bohr radius. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2021, 115, 2, Article number 44. https://doi.org/10.1007/s13398-020-00986-1
  • K. C. Ciesielski, T. Natkaniec, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Additivity Coefficients for all Classes in the Algebra of Darboux-Like Maps on R. Results in Mathematics.
    2021, 76, 1, Article number 7. https://doi.org/10.1007/s00025-020-01287-0
  • J. Fernández-Sánchez, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda, W. Trutschnig. Lineability, differentiable functions and special derivatives. Banach Journal of Mathematical Analysis. 2021, 15, 1, Article number 18. https://doi.org/10.1007/s43037-020-00103-9
  • P. Jiménez-Rodríguez, M. E. Martínez-Gómez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. Generalizing Multiplicative Convex Functions. Journal of Convex Analysis. 2021, 28, 3. https://www.scopus.com/record/display.uri?eid=2-s2.0-85099662277&origin=SingleRecordEmailAlert&dgcid=raven_sc_author_en_us_email&txGid=4489e18cd4415633edf288d507c0d88e
  • G. A. Muñoz-Fernández, J. M. Seoane, J. B. Seoane-Sepúlveda. A SIR-type model describing the successive waves of COVID-19. Chaos, Solitons and Fractals. 2021, 144, Article number 110682. https://doi.org/10.1016/j.chaos.2021.110682
  • R. Campoamor-Stursberg, F. Oviaño. Algorithmic construction of solvable rigid Lie algebras determined by generating functions. Linear and Multilinear Algebra. 2020. https://doi.org/10.1080/03081087.2020.1720577
  • R. Campoamor-Stursberg. Trace formulas for the Casimir operators of the unextended Schrödinger algebra S(N). Journal of Mathematical Physics. 2020, 61(4), 043508. https://doi.org/10.1063/1.5141091
  • R. Campoamor-Stursberg. The method of virtual copies and contractions of simple Lie algebras. Journal of Physics Conference Series. 2020, 1612, 012006. https://doi.org/10.1088/1742-6596/1612/1/012006
  • R. Campoamor-Stursberg. Lie-Point symmetries preserved by derivative. Geometry, Integrability and Quantization. 2020, 21, 75-88. https://doi.org/10.7546/giq-21-2020-75-88
  • D. Azagra, J. Ferrera, J. Gómez Gil, C. Mudarra. Extensions of convex functions with prescribed subdifferentials. Studia Mathematica. 2020, 253, 2, 199-213. https://doi.org/10.4064/sm181212-17-5
  • G. Beer, L. C. Garcí­a-Lirola, M. I. Garrido. Stability of Lipschitz-type functions under pointwise product and reciprocation. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2020, 114 (3), art. no. 120, . DOI: https://doi.org/10.1007/s13398-020-00847-x
  • R. Monjo, R. Campoamor-Stursberg. Lagrangian density and local symmetries of inhomogeneous hyperconical universes. Classical and Quantum Gravity. 2020, 37 (20), 205015. https://doi.org/10.1088/1361-6382/abadaf
  • A. Daniilidis, J. A. Jaramillo, F. Venegas M. Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds. Journal of Functional Analysis. 2020, 279, 108662. https://doi.org/10.1016/j.jfa.2020.108662
  • J. Khodabandehlou, S. Maghsoudi, J. B. Seoane-Sepúlveda. Lineability and algebrability within p−adic function spaces. Bull. Belg. Math. Soc. Simon Stevin. 2020, 27. https://projecteuclid.org/euclid.bbms/1608779382
  • J. Fernández-Sánchez, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda, W. Trutschnig. Lineability and integrability in the sense of Riemann, Lebesgue, Denjoy, and Khintchine. Journal of Mathematical Analysis and Applications. 2020, 492, 1, 124433, 16. https://doi.org/10.1016/j.jmaa.2020.124433
  • G. Araújo, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Sharp Bernstein inequalities using convex analysis techniques. Math. Inequal. Appl. 2020, 23, 2, 725–750. https://doi.org/10.7153/mia-2020-23-61
  • L. Bernal-González, J. Fernández-Sánchez, J. B. Seoane-Sepúlveda, W. Trutschnig. Highly tempering infinite matrices II: From divergence to convergence via Toeplitz-Silverman matrices. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas.2020, 114, 4, 202. https://link.springer.com/article/10.1007%2Fs13398-020-00934-z
  • L. Bernal-González, J. López-Salazar, J. B. Seoane-Sepulveda. Holomorphic surjectivity near the boundary: topological and algebraic genericity. Linear and Multilinear Algebra. 2020, 68, 7,  1434-1456. DOI: https://doi.org/10.1080/03081087.2018.1545830
  • L. Bernal-González, G. A. Muñoz-Fernández, D. L.Rodrí­guez-Vidanes, J. B. Seoane-Sepúlveda. A complete study of the geometry of 2-homogeneous polynomials on circle sectors. Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas. 2020, 114 (3), art. no. 160. DOI: https://doi.org/10.1007/s13398-020-00892-6
  • J. Fernández-Sánchez, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Obtaining algebrability in subsets of real functions. Publ. Math. Debrecen. 2020, 96, 1-2, 231–244. https://doi.org/10.5486/PMD.2020.8660
  • L. Bernal-González, H. J. Cabana-Méndez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. On the dimension of subspaces of continuous functions attaining their maximum finitely many times. Trans. Amer. Math. Soc. https://doi.org/10.1090/tran/8054 
  • A. Bonilla, G. A. Muñoz-Fernández, J. A. Prado-Bassas, J. B. Seoane-Sepúlveda. Hausdorff and Box dimensions of continuous functions and lineability. Linear and Multilinear Algebra. Published online: 06 May 2019 https://doi.org/10.1080/03081087.2019.1612832
  • P. Jiménez-Rodríguez, M. E. Martínez-Gómez, G. A. Muñoz-Fernández, J. B. Seoane-Sepúlveda. Describing Multiplicative Convex Functions. Journal of Convex Analysis. http://www.heldermann-verlag.de/jca/jca27/jca2081-a.pdf
  • L. Bernal-González, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepúlveda. Algebraic genericity within the class of sup-measurable functions. J. Math. Anal. Appl. 2020, 483 (2020), no. 1, 123576. https://doi.org/10.1016/j.jmaa.2019.123576 
  • G. Beer, M. I. Garrido. Real-valued Lipschitz functions and metric properties of functions. Journal of Mathematical Analysis and Applications. 2020, 486, 1, 123839. https://www.sciencedirect.com/science/article/pii/S0022247X20300019 
  • J. Ferrera, J. Gómez Gil. Differentiability of the functions of the generalized Takagi Class. Revista Matemática Complutense. 2020, 33, 465–493. DOI link: https://doi.org/10.1007/s13163-019-00326-x
  • G. Araujo, P. H. Enflo, G. A. Muñoz-Fernández, D. L. Rodríguez-Vidanes, J. B. Seoane-Sepulveda. Quantitative and qualitative estimates on the norm of products of polynomials. Israel Journal of Mathematics. 2020, 236 (2), 727-745. DOI: https://doi.org/10.1007/s11856-020-1987-y

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