S. Farhangi

activity

20142026

most citedA generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages

2 citations · 4 across the 14 of their papers we have counts for

collaborators

15 papers

math.CO2026

$2$ -large sets are sets of nil-Bohr recurrence

Ryan Alweiss, Sohail Farhangi

A set $S$ of positive integers is $2$ -large if every two-coloring contains arbitrarily long monochromatic arithmetic progressions with common difference in $S$ . We prove that every…

math.DS2026

Solutions to 6 problems in recurrence and Van der Corput sets

Sohail Farhangi, Saúl Rodríguez Martín

We present solutions to six problems concerning sets of nice recurrence and van der Corput (vdC) sets. We answer a question of Moreira, repeated by Fish and Skinner, by showing tha…

math.DS2026

Multipliers and Disjointness from Mixing

Sohail Farhangi, Joel Moreira, Rigoberto Zelada

In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking…

math.DS2025

The Theory of Normality for Dynamically Generated Cantor Series Expansions

Sohail Farhangi, Bill Mance

The theory of normality for base $g$ expansions of real numbers in $[0, 1)$ is rich and well developed. Similar theories have been developed for many other numeration systems, such…

math.FA2025

On the Jacobs-de Leeuw-Glicksberg decomposition for representations of semigroups

Micky Barthmann, Sohail Farhangi, Yulia Kuznetsova

We develop a systematic study of the Jacobs-de Leeuw-Glicksberg decomposition for JdLG-admissible semigroup representations on Banach spaces, with emphasis on its structural, ergod…

math.LO2024

Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem

Sohail Farhangi, Steve Jackson, Bill Mance

We show that several sets of interest arising from the study of partition regularity and density Ramsey theory of polynomial equations over integral domains are undecidable. In par…

math.DS2024

Asymptotic dynamics on amenable groups and van der Corput sets

Sohail Farhangi, Robin Tucker-Drob

We answer a question of Bergelson and Lesigne by showing that the notion of van der Corput set does not depend on the Følner sequence used to define it. This result has been discov…

math.FA2024

Uniform vector-valued pointwise ergodic theorems for operators

Micky Barthmann, Sohail Farhangi

We prove a uniform vector-valued Wiener-Wintner Theorem for a class of operators that includes compositions of ergodic Koopman operators with contractive multiplication operators.…

math.GR2023

Koopman representations for positive definite functions

Sohail Farhangi

We show that for any locally compact second countable group $G$ and any continuous positive definite function $ϕ : G \to C$ , there exists an ergodic measure preserving…

math.DS2023

Van der Corput's difference theorem for amenable groups and the left regular representation

Sohail Farhangi

We establish a connection between two variants of van der Corput's Difference Theorem (vdCDT) for countably infinite amenable groups $G$ and the ergodic hierarchy of mixing propert…

math.DS2023★ 2 cited

A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages

Sohail Farhangi

We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between s…

math.DS2021★ 1 cited

Pointwise Ergodic Theorems for Higher Levels of Mixing

Sohail Farhangi

We prove strengthenings of the Birkhoff Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing syste…

math.DS2021

A generalization of van der Corput's Difference Theorem

Sohail Farhangi

We prove a generalization of van der Corput's Difference Theorem in the theory of uniform distribution by establishing a connection with unitary operators that have Lebesgue spectr…

math.CO2021

On The Partition Regularity of $a x + b y = c w^{m} z^{n}$

Sohail Farhangi, Richard Magner

Csikvári, Gyarmati, and Sárközy showed that the equation $x + y = z^{2}$ is not partition regular (PR) over $N$ and asked if the equation $x + y = w z$ is PR over $N$ . B…

math.OA2014★ 1 cited

Induced representations of Hilbert $C^{*}$ -modules

Gh. Abbaspour Tabadkan, S. Farhangi

In this paper, we define the notion of induced representations of a Hilbert $C^{*}$ -module and we show that Morita equivalence of two Hilbert modules (in the sense of Moslehian and…

2-large sets are sets of nil-Bohr recurrence

Solutions to 6 problems in recurrence and Van der Corput sets

Multipliers and Disjointness from Mixing

The Theory of Normality for Dynamically Generated Cantor Series Expansions

On the Jacobs-de Leeuw-Glicksberg decomposition for representations of semigroups

Undecidability in the Ramsey theory of polynomial equations and Hilbert's tenth problem

Asymptotic dynamics on amenable groups and van der Corput sets

Uniform vector-valued pointwise ergodic theorems for operators

Koopman representations for positive definite functions

Van der Corput's difference theorem for amenable groups and the left regular representation

A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages

Pointwise Ergodic Theorems for Higher Levels of Mixing

A generalization of van der Corput's Difference Theorem

On The Partition Regularity of ax+by=cwmzn

Induced representations of Hilbert C∗-modules

$2$ -large sets are sets of nil-Bohr recurrence

On The Partition Regularity of $a x + b y = c w^{m} z^{n}$

Induced representations of Hilbert $C^{*}$ -modules