7 papers · 1 filter
On the structure of polynomial multicorrelation sequences arising from nilpotent actions
Jovan Andreevski, Felipe Hernández
We prove that every polynomial multicorrelation sequence arising from nilpotent actions admits a decomposition into a generalized nilsequence and a null-sequence. This resolves a l…
Infinite prime sumsets in structured and -uniform sets
Felipe Hernández, Tristán Radić
By introducing new ergodic-theoretic techniques in nilsystems, we determine which infinite sumset configurations occur in -uniform and Nil-Bohr sets. To be more precise, ou…
Structure and Spectrum of Nonergodic Nilsystems
Felipe Hernández
We study Host-Kra factors and the spectral type of nilsystems, without assuming ergodicity. In the ergodic case, it is known that the spectral type splits into a discrete component…
On density analogs of Hindman's finite sums theorem
Felipe Hernández, Ioannis Kousek, Tristán Radić
For any set of natural numbers with positive upper Banach density, we show the existence of an infinite set and sequences …
Infinite linear patterns in sets of positive density
Felipe Hernández
In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Sz…
Multiple Polynomial Recurrence in Weyl Systems
Felipe Hernández
In this work we give a full characterization of sets of multiple polynomial recurrence in Weyl systems, which are ergodic unipotent affine transformations on products of tori and f…
On recurrence for -Weyl systems
Sebastián Donoso, Felipe Hernández, Alejandro Maass
We study the topological recurrence phenomenon of actions of locally compact abelian groups on compact metric spaces. In the case of -actions we develop new technique…