Author

J. Seoane-Sepúlveda

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Open access 2023

On Special Partitions of [0,1] and Lineability within Families of Bounded Variation Functions

We show that there exist large algebraic structures (vector spaces, algebras, closed subspaces, etc.) formed entirely (except for 0), on one hand, by singular, nowhere monotonic functions on [0,1] and, on the other hand, by absolutely continuous nowhere monotonic functions. Several tools, of independent interest, rel...

L. Bernal-González, J. Fernández-Sánchez, J. Seoane-Sepúlveda et al. · Journal of Convex Analysis · 1 citation

Preprint Sep 2026

A Levin-Milman theorem for Young variation

In 1940, Levin\footnotemark[1] and Milman proved that a closed linear subspace of $C[0,1]$ whose elements all have bounded Jordan variation must be finite-dimensional. We prove its analogue for variation in the sense of Young and, more generally, for every finite-valued nondecreasing gauge $\varphi:[0,\infty)\to[0,\inf...

N. Albuquerque, D. Bugajewska, E. Demétrio et al. · 0 citations