Related papers: A quantitative Balian-Low theorem for higher dimen…

We show two results. First, a refinement of Freiman's theorem: if A is a finite set of integers and |A+A| < K|A|, then A is contained in a multidimensional progression of dimension at most O(K^{7/4} log^3K) and size at most exp(O(K^{7/4}…

We consider the functions that bound the dimensions of finite-dimensional associative or Lie algebras in terms of the dimensions of their commutative subalgebras. It is proved that these functions have quadratic growth. As a result, we also…

In this article, we prove a quantitative version of Carleson's $\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the…

This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and…

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

Using analyticity of the vacuum wave-functional under complex scalings, the vacuum of a quantum field theory may be reconstructed from a derivative expansion valid for slowly varying fields. This enables the eigenvalue problem for the…

We provide a Kingman-like Theorem for arbitrary finite measures and a version of Birkhoff's Theorem for bounded observable. As an application, we show that Birkhoff's limit exists for some continuous observable, in an example of Bowen.

We give a complementary generalization of the extensions of Bonnet-Myers theorem obtained by Calabi and also Cheeger-Gromov-Taylor.

By extending the Johnson--Barron projection method from one dimension to high dimensions and utilizing a Wang type dimension-free Harnack inequality, we obtain a new quantitative bound for the entropic central limit theorem under the…

We find new relations for the non-universal part of the Yang-Mills amplitudes by combining the KLT-relation and the soft behavior of gauge and gravity amplitudes. We also extend the relations to include contributions from effective…

Newtonian limit of Extended Theories of Gravity (in particular, higher--order and scalar--tensor theories) is theoretically discussed taking into account recent observational and experimental results.

We derive curvature estimates for minimal submanifolds in Euclidean space for arbitrary dimension and codimension via Gauss map. Thus, Schoen-Simon-Yau's results and Ecker-Huisken's results are generalized to higher codimension. In this way…

In this paper we extend some results obtained by Artamonov and Sabitov for quantum polynomials to skew quantum polynomials and quasi-commutative bijective skew PBW extensions. Moreover, we find a counterexample to the conjecture proposed in…

New proofs of theorems on the multifractal formalism are given. They yield results even at points q for which Olsen's functions b(q) and B(q) differ. Indeed, we provide an example of measure for which functions b and B differ and for which…

We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.

We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.

A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.

We prove several extensions of the Erdos-Fuchs theorem.

We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…

We study quantized enveloping algebras called twisted Yangians. They are analogues of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to…