Related papers: Triviality of the Peripheral Point Spectrum

For cofinite Kleinian groups, with finite-dimensional unitary representations, we derive the Selberg trace formula. As an application we define the corresponding Selberg zeta-function and compute its divisor, thus generalizing results of…

Let $X$ be an arbitrary set and let $T(X)$ denote the full transformation monoid on $X$. We prove that an element of $T(X)$ is unit-regular if and only if it is semi-balanced. For infinite $X$, we discuss regularity of the submonoid of…

We determine the local spectrum of a central element of the complexified universal enveloping algebra of a compact connected Lie group at a smooth function as an element of L^p(G). Based on this result we establish a corresponding local…

In this paper we start studying spectral properties of the Fourier-Stieltjes algebras, largely following Zafran's work on the algebra of measures on a locally compact group. We show that for a large class of discrete groups the Wiener-Pitt…

Let $ \Lambda (s) := \Gamma(s+1)\, (1-2^{1-s}) \, \zeta(s) $, and denote its set of zeros by $ Z_\Lambda := Z_\zeta \cup Z_\mathrm{p} $, where $ Z_\zeta $ consists of the nontrivial zeros of $ \zeta(s) $ and $ Z_\mathrm{p} $ those of the…

We constructed a unitary semigroup $(e^{tA})_{t \geq 0}$ on a Hilbert space and an orthogonal projection $P$ such that the limit $\lim_{n \to \infty} [ e^{\frac{t}{n}A}P ]^n$ does not exist strongly. A similar example with a positive…

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is *very good*. If X in Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G…

We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern…

Let $X$ be a nonempty set, and let $\mathcal{T}_X$ be the full transformation semigroup on $X$. For a partition $\mathcal{P} = \{X_i \;|\; i\in I\}$ of $X$, we consider the semigroup $T(X, \mathcal{P}) = \{f\in \mathcal{T}_X\;|\; \forall…

If F is a surface with boundary, then a finitely generated subgroup without peripheral elements of G = {\pi}_1(F) can be separated from finitely many other elements of G by a finite index subgroup of G corresponding to a finite cover F'…

It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there…

Let $X$ be a Banach space, and $T:[0,\infty)\rightarrow {\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\{T(t)\}_{t\ge 0}\subseteq {% \mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and…

A topological group is (openly) almost-elliptic if it contains a(n open) dense subset of elements generating relatively-compact cyclic subgroups. We classify the (openly) almost-elliptic connected locally compact groups as precisely those…

It is shown that the closure of the set of Fourier coefficients of the Bernoulli convolution $\mu_\theta$ parameterized by a Pisot number $\theta$, is countable. Combined with results of Salem and Sarnak, this proves that for every fixed…

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…

Let $\varepsilon>0$ be a fixed small constant, ${\mathbb F}_p$ be the finite field of $p$ elements for prime $p$. We consider additive and multiplicative problems in ${\mathbb F}_p$ that involve intervals and arbitrary sets. Representative…

A bounded set $\Omega \subset \mathbb{R}^d$ is called a spectral set if the space $L^2(\Omega)$ admits a complete orthogonal system of exponential functions. We prove that a cylindric set $\Omega$ is spectral if and only if its base is a…

For a tuple $A=(A_1,\ A_2,\ ...,\ A_n)$ of elements in a unital algebra ${\mathcal B}$ over $\mathbb{C}$, its {\em projective spectrum} $P(A)$ or $p(A)$ is the collection of $z\in \mathbb{C}^n$, or respectively $z\in \mathbb{P}^{n-1}$ such…

The Hilbert space $\mathcal H$ of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group $F$ via local scale transformations. Given a vector in the canonical dense subspace of…

Fix a prime $p\geq 11$. We show that there exists a positive integer $m$ such that any subset of $\mathbb{F}_p^n\times\mathbb{F}_p^n$ containing no nontrivial configurations of the form $(x,y),(x,y+z),(x,y+2z),(x+z,y)$ must have density…