Related papers: Balian-Low type theorems in finite dimensions

We show that every countable direct system of finite-dimensional real or complex Lie groups has a direct limit in the category of Lie groups modelled on locally convex spaces. This enables us to push all basic constructions of…

A p-adic analogue of the pseudonorm version of the birational Torelli type theorem is obtained via a comparison theorem of image closures. Among other results obtained, we have a criterion for existence of rational points of canonically…

Limit theorems of strong law of large numbers and central limit theorem types are obtained for the compositions of independent identically distributed random unitary channels.

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

We study linear actions of finite groups in small dimensions, up to equivariant birationality.

We study multivariate generalizations of the $q$-central limit theorem, a generalization of the classical central limit theorem consistent with nonextensive statistical mechanics. Two types of generalizations are addressed, more precisely…

We generalize the classical Bernstein theorem concerning the constructive description of classes of functions uniformly continuous on the real line. The approximation of continuous bounded functions by entire functions of exponential type…

We offer new proofs, refinements as well as new results related to classical means of two variables, including the identric and logarithmic means.

Let $\Lambda$ be an artinian ring. Generalizing the Loewy length, we propose the layer length associated with a torsion theory, which is a new measure for finitely generated $\Lambda$-modules.

We give an equivalent finitary reformulation of the classical Shannon-McMillan-Breiman theorem which has an immediate translation to the case of ergodic quantum lattice systems. This version of a quantum Breiman theorem can be derived from…

We classify finite dimensional division real associative $\mathcal{Z}_2$-algebras, introduce composition $\mathcal{Z}_2$-algebras, and extend the Campbell-Baker-Hausdorff series and Lie correspondence in the context of linear Hu-Liu Leibniz…

In this paper, we prove the infinitely many solutions to a class of sublinear Kirchhoff type equations by using an extension of Clark's Theorem established by Zhaoli Liu and Zhi-Qiang Wang.

We study linear and hermitian representations of finite $C_2$-graded groups. We prove that the category of linear representations is equivalent to a category of antilinear representations as an $\infty$-category. We also prove that the…

We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.

In this note, we propose the modular height of an abelian variety defined over a field of finite type over Q. Moreover, we prove its finiteness property.

We study possible Lie and non-classical reductions of multidimensional wave equations and the special classes of possible reduced equations - their symmetries and equivalence classes. Such investigation allows to find many new conditional…

Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…

In this paper we study finite W-algebras for basic classical superalgebras and Q(n) associated to the regular even nilpotent coadjoint orbits. We prove that this algebra satisfies the Amitsur-Levitzki identity and therefore all its…

We give a sufficient criterion for complex analyticity of nonlinear maps defined on direct limits of normed spaces. This tool is then used to construct new classes of (real and complex) infinite dimensional Lie groups: (a) groups of germs…

We present finitary formulations of two well known results concerning infinite series, namely Abel's theorem, which establishes that if a series converges to some limit then its Abel sum converges to the same limit, and Tauber's theorem,…