Related papers: Noncommutative multi-parameter Wiener-Wintner type…
In 1967, Arveson invented a non-commutative generalization of classical $H^{\infty},$ known as finite maximal subdiagonal subalgebras, for a finite von Neumann algebra $\mathcal M$ with a faithful normal tracial state $\tau$. In 2008,…
Using tools from the theory of optimal transport, we establish several results concerning isometric actions of amenable topological groups with potentially unbounded orbits. Specifically, suppose $d$ is a compatible left-invariant metric on…
Choosing the optimal observable to model dynamical systems for which we do not know the driving equations is nearly always an ad hoc art. Takens' Delay Embedding Theorem guarantees a diffeomorphism between delay-coordinate vectors built…
We develop further our fibre bundle construct of non-commutative space-time on a Minkowski base space. We assume space-time is non-commutative due to the existence of additional non-commutative algebraic structure at each point x of…
The main goal of this paper is twofold. First, it characterizes the existence of positive periodic solutions for a general class of weighted periodic-parabolic logistic problems of degenerate type (see (1.1)). This result provides us with…
We advance a variational method to prove qualitative properties such as symmetries, monotonicity, upper and lower bounds, sign properties, and comparison principles for a large class of doubly-nonlinear evolutionary problems including…
We deal with the boundedness properties of higher order commutators related to some generalizations of the multilinear fractional integral operator of order $m$, $I_\alpha ^m$, from a product of weighted Lebesgue spaces into adequate…
We establish a weighted inequality for fractional maximal and convolution type operators, between weak Lebesgue spaces and Wiener amalgam type spaces on $ \mathbb R $ endowed with a measure which needs not to be doubling.
We study the properties of quasi-distributions or Wigner measures in the context of noncommutative quantum mechanics. In particular, we obtain necessary and sufficient conditions for a phase-space function to be a noncommutative Wigner…
We study a class of homeomorphisms of surfaces collectively known as linked-twist maps. We introduce an abstract definition which enables us to give a precise characterisation of a property observed by other authors, namely that such maps…
We establish weak-type $(1,1)$ bounds for the maximal function associated with ergodic averaging operators modeled on a wide class of thin deterministic sets $B$. As a corollary we obtain the corresponding pointwise convergence result on…
In 2016 and 2017, Haihui Fan, Don Hadwin and Wenjing Liu proved a commutative and noncommutative version of Beurling's theorems for a continuous unitarily invariant norm $\alpha $ on $L^{\infty}(\mathbb{T},\mu)$ and tracial finite von…
We present a novel class of real symmetric matrices in arbitrary dimension $d$, linearly dependent on a parameter $x$. The matrix elements satisfy a set of nontrivial constraints that arise from asking for commutation of pairs of such…
One presents a phase-space noncommutative extension of Quantum Cosmology in the context of a Kantowski-Sachs (KS) minisuperspace model. We obtain the Wheeler-DeWitt (WDW) equation for the noncommutative system through the ADM formalism and…
In this article, we prove maximal inequality and ergodic theorems for state preserving actions on von Neumann algebra by an amenable, locally compact, second countable group equipped with the metric satisfying the doubling condition. The…
In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schr\"odinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost…
The ergodic decomposition theorem is a cornerstone result of dynamical systems and ergodic theory. It states that every invariant measure on a dynamical system is a mixture of ergodic ones. Here we formulate and prove the theorem in terms…
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 sequences of vectors in the first Hilbert space with a vector…
We give explicit $C^1$-open conditions that ensure that a diffeomorphism possesses a nonhyperbolic ergodic measure with positive entropy. Actually, our criterion provides the existence of a partially hyperbolic compact set with…
We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type…