Related papers: Balian-Low type theorems in finite dimensions

Some assertions in harmonic analysis on the infinite dimensional torus are stated and their equivalence to Riemann hypothesis is proved.

We introduce the theory of local minimal models for Kan simplicial manifolds, which provide the appropriate generalization of minimal Kan simplicial sets to geometric contexts. We use this to obtain the first proof of Lie's third theorem…

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

We show that a minimal ideal of a finite-dimensional Lie algebra is either simple or abelian.

This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of weakly nonlinear and monotone operators defined on spaces of…

We prove a quantitative Borg-Levinson theorem for a large class of unbounded potentials. We give a detailed proof when the dimension of the space is greater than or equal to five. We also indicate the modifications necessary to cover lower…

We prove completeness for the main examples of infinite-dimensional Lie groups and some related topological groups.

We quantize abelian Yang-Mills theory on Riemannian manifolds with boundaries in any dimension. The quantization proceeds in two steps. First, the classical theory is encoded into an axiomatic form describing solution spaces associated to…

Banach's fixed point theorem in linear n-normed space is being developed. Also, we present several theorems on fixed points in linear n-normed space.

It is shown, that extended particle-like objects should infinitely long collapse into some discontinuous configurations of the same topology, but vanishing mass. Analytic results concerning the general properties and asymptotic rates of…

Let $W$ denote the $n$-dimensional affine space over the finite field $\mathbb F_q$. We prove here a Bollob\'as-type upper bound in the case of the set of affine subspaces. We give a construction of a pair of families of affine subspaces,…

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…

A $(d-1)$-dimensional simplicial complex is called balanced if its underlying graph admits a proper $d$-coloring. We show that many well-known face enumeration results have natural balanced analogs (or at least conjectural analogs).…

We proof some basic tools about spaces of H"older-continuous functions between (in general infinite dimensional) Banach spaces and use them to construct new examples of infinite dimensional (LB)-Lie groups.

We prove that if a linear equation, whose coefficients are continuous rational functions on a nonsingular real algebraic surface, has a continuous solution, then it also has a continuous rational solution. This is known to fail in higher…

We prove a Lucas-type congruence for q-Delannoy numbers.

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.

The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no…

We establish a relative Bertini type theorem for multiplier ideal sheaves. Then we prove a relative version of the Koll\'ar--Nadel type vanishing theorem as an application.

We develop a Belyi type theory that applies to Klein surfaces, i.e. (possibly non-orientable) surfaces with boundary which carry a dianalytic structure. In particular we extend Belyi's famous theorem from Riemann surfaces to Klein surfaces.