C. D. Bernardi

activity

20192026

collaborators

8 papers

math.FA2026

Tilings and coverings by balls in $ℓ_{1}$

Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1

A famous result of Klee from 1981 is that the Banach space $ℓ_{1} (κ)$ admits a disjoint tiling by balls of radius $1$ , for all cardinals $κ$ with $κ^{ω} = κ$ . Klee also observed that…

math.FA2026

Extending quasiconvex functions from uniformly convex sets

Carlo Alberto De Bernardi, Libor Veselý

Let $X$ be a normed space of a finite dimension at least two, and $C ⊊ X$ a closed convex set with nonempty interior. We are interested in extending Lipschitz quasiconvex f…

math.FA2026

Packings in classical Banach spaces

Carlo Alberto De Bernardi, Tommaso Russo, Şeyda Sezgek +1

We obtain several new results on the simultaneous packing and covering constant $γ (X)$ of a Banach space $X$ , and its lattice counterpart $γ^{*} (X)$ . Th…

math.OC2025

Characterization of regularity via variational stability of alternating projections sequences

Francesco Battistoni, Aris Daniilidis, Carlo Alberto De Bernardi +1

The notion of regular pair $(A, B)$ for two nonempty closed convex subsets $A$ and~ $B$ of a Hilbert space $\H$ was introduced by Borwein and Bauschke in 1993 to ensure convergence (…

math.FA2025

Lattice tilings of Hilbert spaces

Carlo Alberto De Bernardi, Tommaso Russo, Jacopo Somaglia

We construct a bounded and symmetric convex body in $ℓ_{2} (Γ)$ (for certain cardinals $Γ$ ) whose translates yield a tiling of $ℓ_{2} (Γ)$ . This answers a question due to Fonf and…

math.FA2025

Some remarks on almost locally uniformly rotund points

Carlo Alberto De Bernardi, Jacopo Somaglia

We study the relations between different notions of almost locally uniformly rotund points that appear in literature. We show that every non-reflexive Banach space admits an equiva…

math.FA2020

A note on point-finite coverings by balls

Carlo Alberto De Bernardi

We provide an elementary proof of a result by V.P.~Fonf and C.~Zanco on point-finite coverings of separable Hilbert spaces. Indeed, by using a variation of the famous argument intr…

math.OC2019

A variational approach to the alternating projections method

Carlo A. De Bernardi, Enrico Miglierina

The 2-sets convex feasibility problem aims at finding a point in the nonempty intersection of two closed convex sets $A$ and $B$ in a Hilbert space $X$ . The method of alternating p…

Tilings and coverings by balls in ℓ1​

Extending quasiconvex functions from uniformly convex sets

Packings in classical Banach spaces

Characterization of regularity via variational stability of alternating projections sequences

Lattice tilings of Hilbert spaces

Some remarks on almost locally uniformly rotund points

A note on point-finite coverings by balls

A variational approach to the alternating projections method

Tilings and coverings by balls in $ℓ_{1}$