Related papers: Approximation by group invariant subspaces

A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…

Crystallographic groups describe the symmetries of crystals and other repetitive structures encountered in nature and the sciences. These groups include the wallpaper and space groups. We derive linear and nonlinear representations of…

In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…

This is a further investigation of our approach to group actions in homological algebra in the settings of homology of {\Gamma}-simplicial groups, particularly of {\Gamma}-equivariant homology and cohomology of {\Gamma}-groups. This…

A group $\Gamma$ is said to be finitely non-co-Hopfian, or renormalizable, if there exists a self-embedding $\varphi \colon \Gamma \to \Gamma$ whose image is a proper subgroup of finite index. Such a proper self-embedding is called a…

Let $\phi: \R^d \longrightarrow \C$ be a compactly supported function which satisfies a refinement equation of the form $\phi(x) = \sum_{k\in\Lambda} c_k \phi(Ax - k),\quad c_k\in\C$, where $\Gamma\subset\R^d$ is a lattice, $\Lambda$ is a…

We introduce a practical construction of group-equivariant and permutation-invariant functions of $N$ variables given a finite-dimensional space stable with respect to the group action. The construction applies to any connected linear Lie…

Let $G$ be a reflection group acting on a vector space $V$ and let $\gamma$ be an automorphism of $V$ normalising $G$. We study how $\gamma$ acts on invariants and covariants (for various representations) of $G$, and properties of its…

Let $\Gamma$ be a countable discrete group. We show that $\Gamma$ has the approximation property if and only if $\Gamma$ is exact and for any operator space $S \subseteq \K(H)$ we have $\Cu(\Gamma)^{\Gamma} \otimes S = (\Cu(\Gamma) \otimes…

In this paper a sampling theory for unitary invariant subspaces associated to locally compact abelian (LCA) groups is deduced. Working in the LCA group context allows to obtain, in a unified way, sampling results valid for a wide range of…

This work is devoted to the study of Bessel and Riesz systems of the type $\big\{L_{\gamma}\mathsf{f}\big\}_{\gamma\in \Gamma}$ obtained from the action of the left regular representation $L_{\gamma}$ of a discrete non abelian group…

Let $\Gamma $ be an infinite discrete group and $\mathsf{A}\subset \Gamma $ a nonempty finite subset. The set of permutations $\sigma $ of $\Gamma $ such that $s^{-1}\sigma (s)\in \mathsf{A}$ for every $s\in \Gamma $ can be identified with…

We define spectral gap actions of discrete groups on von Neumann algebras and study their relations with invariant states. We will show that a finitely generated ICC group $\Gamma$ is inner amenable if and only if there exist more than one…

An invariant random subgroup $H \leq G$ is a random closed subgroup whose law is invariant to conjugation by all elements of $G$. When $G$ is locally compact and second countable, we show that for every invariant random subgroup $H \leq G$…

This paper concerns the non-commutative analog of the Normal Subgroup Theorem for certain groups. Inspired by Kalantar-Panagopoulos, we show that all $\Gamma$-invariant subalgebras of $L\Gamma$ and $C^*_r(\Gamma)$ are ($\Gamma$-)…

Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…

We construct a $GL$-invariant measure on a semi-infinite Grassmannian over a finite field, describe the natural group of symmetries of this measure, and decompose the space $L^2$ over the Grassmannian on irreducible representations. The…

In this paper we study the action of a countable group $\Gamma$ on the space of orders on the group. In particular, we are concerned with the invariant probability measures on this space, known as invariant random orders. We show that for…

The aim of this paper is to give a generalization of the theory equivariant functions, initiated in [17, 4], to arbitrary subgroups of PSL2(R). We show that there is a deep relation between the geometry of these groups and some analytic and…