Publications

Journal Articles

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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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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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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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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