Related papers: Lacunary Fourier series and a qualitative uncertai…

We define the notion of a (linearly reductive) center for a linearly reductive quantum group, and show that the quotient of a such a quantum group by its center is simple whenever its fusion semiring is free in the sense of Banica and…

It is a basic fact in infinite-dimensional Lie theory that the unit group G(A) of a continuous inverse algebra A is a Lie group. We describe criteria ensuring that the Lie group G(A) is regular in Milnor's sense. Notably, G(A) is regular if…

The U(1) gauge theory on a space with Lie type noncommutativity is constructed. The construction is based on the group of translation in Fourier space, which in contrast to space itself is commutative. In analogy with lattice gauge theory,…

In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We show that a global variant of this observed phenomenon holds in…

The infinitesimal counterpart of a Lie groupoid is its Lie algebroid. As a vector bundle, it is given by the source vertical tangent bundle restricted to the identity bisection. Its sections can be identified with the invariant vector…

We determine when an arithmetic subgroup of a reductive group defined over a global function field is of type FP_\infty by comparing its large-scale geometry to the large-scale geometry of lattices in real semisimple Lie groups.

The uncertainty principle lies at the heart of quantum physics, and is widely thought of as a fundamental limit on the measurement precisions of incompatible observables. Here we show that the traditional uncertainty relation in fact…

Let $G$ be the group of $\mathbb R$--points of a semisimple algebraic group $\mathcal G$ defined over $\mathbb Q$. Assume that $G$ is connected and noncompact. We study Fourier coefficients of Poincar\' e series attached to matrix…

A classical result due to Levinson characterizes the existence of non-zero functions defined on a circle vanishing on an open subset of the circle in terms of the pointwise decay of their Fourier coefficients [13]. We prove certain analogue…

A positive definite and integral quadratic form $f$ is called irrecoverable if there is a quadratic form $F$ such that it represents all proper subforms of $f$, whereas it does not represent $f$ itself. In this case, $F$ is called an…

Let $\mathcal{F}$ be a set of finite groups. A finite group $G$ is called an \emph{$\mathcal{F}$-cover} if every group in $\mathcal{F}$ is isomorphic to a subgroup of $G$. An $\mathcal{F}$-cover is called \emph{minimal} if no proper…

In this paper we generalize Bochkariev's theorem, which states that for any uniformly bounded orthonormal system $\Phi$, there exists a Lebesgue integrable function such that the Fourier series of it with respect to system $\Phi$ diverge on…

Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $\chi$ of $G$ such that $\chi(g) = 0$; in this case, we say that the conjugacy class of $g$ is a vanishing conjugacy…

We prove a Bochner type vanishing theorem for compact complex manifolds $Y$ in Fujiki class $\mathcal C$, with vanishing first Chern class, that admit a cohomology class $[\alpha] \in H^{1,1}(Y,\mathbb R)$ which is numerically effective…

We generalize Lewis's result about a central series associated with the vanishing off subgroup. We write $V_{1}=V(G)$ for the vanishing off subgroup of $G$, and $V_{i}=[V_{i-1},G]$ for the terms in this central series. Lewis proved that…

Our purpose is to investigate all defined Poincar\'e series associated with multi-index filtrations and value semigroups of curve singularities---not necessarily complex---with regard to the property of forgetting variables, i.e., by making…

We show that a Lie group $G$ admitting a bi-invariant distance must be the product $G=H\times K$ of an abelian group $H$ and a compact group $K$ with discrete center. Moreover, the distance in $G$ must come from the infima of lengths of…

Let G be a locally compact Hausdorff group in which every element is of finite order, and let P(G) denote the class of all regular probability measures on G. In this note, it is observed that a characterization of algebraically regular…

In the Euclidean space it is known that a function $f\in L^2$ of a ball, with vanishing average,is the divergence of a vector field $F\in L^2$ with$$\| F\|\_{ L^2(B)} \le C \|f\|\_{L^2(B)}.$$In this Note we prove a similar result in any…

We extend a classical theorem of Courr\`{e}ge to Lie groups in a global setting, thus characterising all linear operators on the space of smooth functions of compact support that satisfy the positive maximum principle. We show that these…