相关论文: Semigroup Growth Bounds

A numerical semigroup is an additive submonoid of the natural numbers with finite complement. The size of the complement is called the genus of the semigroup. How many numerical semigroups have genus equal to $g$? We outline Zhai's proof of…

We give a new upper bound on the Selberg zeta function for a convex co-compact Schottky group acting on $ {\mathbb H}^{n+1}$: in strips parallel to the imaginary axis the zeta function is bounded by $ \exp (C |s|^\delta) $ where $ \delta $…

Given a matrix $A\in SL(N,\Z)$, form the semidirect product $G=\Z^N\rtimes_A \Z$ where the $\Z$ factor acts on $\Z^N$ by $A$. Such a $G$ arises naturally as the fundamental group of an $N$-dimensional torus bundle which fibers over the…

We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of…

In this paper we consider an initial-boundary value problem related to some network dynamics where the underlying graph has unbounded edges. We show that there exists a C0-semigroup for this problem using a general result from the…

The purpose of this note is to review some recent results concerning the pseudospectra and the eigenvalues asymptotics of non-selfadjoint semiclassical pseudo-differential operators subject to small random perturbations.

We study the LEF growth function of a finitely generated LEF group $\Gamma$, which measures the orders of finite groups admitting local embeddings of balls in a word metric on $\Gamma$. We prove that any sufficiently smooth increasing…

We consider a non-self-adjoint pseudodifferential operator in the semi-classical limit $(h\to 0)$. The principal symbol is given by p. We know that the resolvent $(z-P)^{-1}$ exists inside the range up to a distance…

In this paper we examine the asymptotic structure of the pseudospectrum of the singular Sturm-Liouville operator $L=\partial_x(f\partial_x)+\partial_x$ subject to periodic boundary conditions on a symmetric interval, where the coefficient…

We obtain explicit upper and lower bounds on the norms of the spectral projections of the non-self-adjoint harmonic oscillator. Some of our results apply to a variety of other families of orthogonal polynomials.

Learned physics simulators are often evaluated by one-step or short-horizon prediction error, but these metrics can miss failures in temporal composition and long-horizon rollout. For autonomous, state-complete systems, exact solution maps…

We propose a new approach to the study of (nonlinear) growth and instability for semilinear evolution equations with compact nonlinearities. We show, in particular, that compact nonlinear perturbations of a linear evolution equation can be…

We obtain the spectral and resolvent estimates for semiclassical pseudodifferential operators with symbol of Gevrey-$s$ regularity, near the boundary of the range of the principal symbol. We prove that the boundary spectrum free region is…

We extend the semigroup approach used in [23,21] to provide alternative proofs of the reconstruction theorem and the multilevel Schauder estimate for singular modelled distributions. As an application of them, we construct the local-in-time…

In this paper, we describe the different spectrums of the {\alpha}-times integrated semigroups by the spectrums of their generators. Specially, essential ascent and descent, upper and lower semi-Fredholm and semi-Browder spectrums.

Motivated by examples from physics and noncommutative geometry, given a generator $A$ of a Gibbs semigroup, we reexamine the relationship between the Schatten class of its resolvents and the behaviour of the norm-trace $\norm{e^{-tA}}_1\,$…

Let $X$ be a nonempty set and $T(X)$ the full transformation semigroup on $X$. For any equivalence relation $E$ on $X$, define a subsemigroup $T_{E^*}(X)$ of $T(X)$ by $$ T_{E^*}(X)=\{\alpha\in T(X):\text{for all}\ x,y\in X, (x,y)\in…

Normal residual finiteness growth measures how well a finitely generated group is approximated by its finite quotients. We show that any linear group $\Gamma \leq \mathrm{GL}_d(K)$ has normal residual finiteness growth asymptotically…

We prove first that the realization $A_{\min}$ of $A:=\mathrm{div}(Q\nabla)-V$ in $L^2(\mathbb{R}^d)$ with unbounded coefficients generates a symmetric sub-Markovian and ultracontractive semigroup on $L^2(\mathbb{R}^d)$ which coincides on…

Given a group G acting on a geodesic metric space, we consider a preferred collection of paths of the space -- a path system -- and study the spectrum of relative exponential growth rates and quotient exponential growth rates of the…