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Posts
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portfolio
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publications
Teoremas de reordenamiento de series
Published in Zubía, 2020
We review results on rearranging terms of series, from \(\mathbb{R}\) to Banach spaces, including Riemann’s rearrangement theorem and the Lévy-Steinitz theorem.
Recommended citation: Bello Hernández, M., Mahillo, A. (2020). Teoremas de reordenamiento de series. Zubía, 37-38, 129-148.
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Catalan Generating Functions for Generators of Uni-parametric Families of Operators
Published in Mediterranean Journal of Mathematics, 2022
We study solutions of the quadratic equation \(AY^2 - Y + I = 0\) where A is the generator of a one-parameter family of operators on a Banach space.
Recommended citation: Mahillo, A., Miana, P.J. Catalan Generating Functions for Generators of Uni-parametric Families of Operators. Mediterr. J. Math. 19, 238 (2022).
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Discrete variational calculus for accelerated optimization
Published in Journal of Machine Learning Research (JMLR), 2023
We introduce variational integrators using Hamilton’s and Lagrange-d’Alembert’s principle to derive optimization methods generalizing Polyak’s heavy ball and Nesterov’s accelerated gradient.
Recommended citation: Campos, C.M., Mahillo, A., Martín de Diego, D. (2023). Discrete variational calculus for accelerated optimization. J. Mach. Learn. Res., 24(25), 1–33.
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A Ritt-Kreiss condition: spectral localization and norm estimates
Published in Studia Mathematica, 2024
We introduce the \((\alpha, \beta)\)-RK condition, a generalization of Ritt and Kreiss operators, and study its spectral properties and power norm estimates.
Recommended citation: Mahillo, A., Rueda, S. (2024). A Ritt-Kreiss condition: spectral localization and norm estimates. Studia Math., 276(2), 171–193.
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End-point maximal regularity for the discrete parabolic Cauchy problem and regularity of non-local operators in discrete Besov spaces
Published in Journal of Differential Equations, 2025
We establish end-point maximal regularity for the discrete heat equation on \(\mathbb{Z}\) and characterize discrete Besov spaces via the fractional powers of the discrete Laplacian.
Recommended citation: Abadias, L., De León-Contreras, M., Mahillo, A. (2025). End-point maximal regularity for the discrete parabolic Cauchy problem and regularity of non-local operators in discrete Besov spaces. J. Differential Equations, 440, Paper No. 113465.
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talks
Funciones generadoras de Catalan para generadores de familias uniparamétricas de operadores
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Generalized discrete Holder spaces
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Spectral properties of the Cesàro operator via C₀-semigroup theory and a note on universality
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Fine Spectral Analysis and Invariant Subspaces of Cesaro-Hardy Operators via C₀-Semigroups
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Análisis espectral y subespacios invariantes de los operadores de Cesàro-Hardy en Lᵖ[0,1]
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teaching
Academic Year 2020-2021
Substitute Professor, Universidad de La Rioja, Departamento de Matemáticas y Computación, 2020
- Logic Mathematics and Computer Science Engineering, 1st year.
- Mathematics II (Probability, statistics and ODEs)
Chemistry, Oenology and Agricultural Engineering, 1st year. - Modeling and Optimization I (Linear programming and Markov chains)
Mathematics Degree, 3rd year.
Academic Year 2022-2023
Teaching Assistant, Universidad de Zaragoza, Departamento de Matemáticas, 2022
Undergraduate Courses
- Analysis I (Real Analysis) Mathematics Degree, 1st year.
Academic Year 2023-2024
Teaching Assistant, Universidad de Zaragoza, Departamento de Matemáticas, 2023
Undergraduate Courses
- Analysis I (Real Analysis) Mathematics Degree, 1st year.
- Analysis II (Multivariable Calculus) Mathematics Degree, 2nd year.
Academic Year 2024-2025
Teaching Assistant, Universidad de Zaragoza, Departamento de Matemáticas, 2024
Undergraduate Courses
- Analysis I (Real Analysis) Mathematics Degree, 1st year.
- Analysis II (Multivariable Calculus) Mathematics Degree, 2nd year.
Fall 2025
Assistant Professor, Universitat de València, Departamento de Análisis Matemático, 2025
Undergraduate Courses
- Analysis I (Real Analysis) Mathematics Degree, 1st year.
- Analysis II (Multivariable Calculus) Mathematics and Physics Degree, 2nd year.
Academic Year 2025-2026
Assistant Professor, Universidad de Cantabria, Departamento de Matemáticas, Estadística y Computación, 2025
Undergraduate Courses
- Numerical Analysis II Mathematics Degree, 3rd year.