Related papers: Stabilization in $H^\infty_{\mathbb{R}}(\mathbb{D}…

We prove ergodicity for random dynamics satisfying some expansion and irreducibility conditions. As a particular application, we show that if $R_1,R_2\in \mathrm{SO}(d+1)$, $d\ge 2$, generate a dense subgroup, then the random dynamics of…

The aim of this paper is to generalize and improve two of the main model-theoretic results of "Stable group theory and approximate subgroups" by E. Hrushovski to the context of piecewise hyperdefinable sets. The first one is the existence…

The stabilization theorem for $A$-Hilbert modules was established by G. G. Kasparov. The equivariant version, in which a locally compact group $H$ acts properly on a locally compact space $Y$, was proved by N. C. Phillips. This equivariant…

Let $f = P[F]$ denote the Poisson integral of $F$ in the unit disk $\mathbb{D}$ with $F$ being absolutely continuous in the unit circle $\mathbb{T}$ and $\dot{F}\in L_p(0, 2\pi)$, where $\dot{F}(e^{it})=\frac{d}{dt} F(e^{it})$ and $p\geq…

Necessary and sufficient conditions on the system of positive numbers $ M_{k_1}, M_{k_2}, M_{k_3}, M_{k_4}$, $0= k_1<k_2<k_3=r-2$, $k_4 = r$, which guarantee the existence of a function $x\in L_{\infty,\infty}^r(R)$, such that…

On a smooth, closed Riemannian manifold $\left(M,g\right)$ of dimension $n\ge3$, we consider the stationary Schr\"odinger equation $\Delta_gu+h_0u=\left|u\right|^{2^*-2}u$, where $\Delta_g:=-\text{div}_g\nabla$, $h_0\in C^1\left(M\right)$…

This paper investigates sharp stability estimates for the fractional Hardy-Sobolev inequality: $$\mu_{s,t}\left(\mathbb{R}^N\right) \left(\int_{\mathbb{R}^N} \frac{|u|^{2^*_s(t)}}{|x|^t} \,{\rm d}x \right)^{\frac{2}{2^*_s(t)}} \leq…

Examples are constructed of infinite-dimensional subspaces $V\subset L^2(\mu)$ with the property that for any $f,g\in V$, if $|f|$ is approximately equal to $|g|$ with respect to the $L^2$ norm, then there exists a unimodular scalar $z$…

If matrices almost satisfying a group relation are close to matrices exactly satisfying the relation, then we say that a group is matricially stable. Here "almost" and "close" are in terms of the Hilbert-Schmidt norm. Using tracial 2-norm…

Let $f: T\to \{ 0,1 \}$ be a Boolean function on the Boolean half-slice, $T$, \ie elements of $\{0,1\}^n$ with Hamming weight $n/2$. We show that if $f(x)+f(y)=f(x+y)$ holds with probability $\frac{1+\delta}{2}$ over a uniform pair $(x,y)$…

Given an infinite reductive algebraic group $G$, we consider $G$-equivariant coherent sheaves with prescribed multiplicities, called $(G,h)$-constellations, for which two stability notions arise. The first one is analogous to the…

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…

In this paper, we introduce the following concept which generalizes known definitions of multiplicative and additive $D$-stability, Schur $D$-stability, $H$-stability, $D$-hyperbolicity and many others. Given a subset ${\mathfrak D} \subset…

Given a prime number $p$ and a positive integer $m$, we provide a family of diagonal hypersurfaces $\{ f_n \}_{n = 1}^{\infty}$ in $m$ variables, for which the denominator of $\text{ fpt } (f_{n})$ (in lowest terms) is always $p$ and whose…

In this work, we summarize the linearization method to study the Heisenberg Uncertainty Principles, and explain that the same approach can be used to handle the stability problem. As examples of application, combining with spherical…

This paper is devoted to the study of semi-stable radial solutions $u\notin H^1(B_1)$ of $-\Delta u=f(u) \mbox{in} \overline{B_1}\setminus \{0\}=\{x\in \mathbb{R}^N : 0<\vert x\vert\leq 1\}$, where $f\in C^1(\mathbb{R})$ and $N\geq 2$. We…

In this paper the following implication is verified for certain basic algebraic curves: if the additive real function $f$ approximately (i.e., with a bounded error) satisfies the derivation rule along the graph of the algebraic curve in…

We will study homological stability of the diffeomorphism groups of the manifolds $W_{g,1}:=D^{2n} \# (S^n \times S^n)^{\#g }$ using $E_k$-algebras. This will lead to new improvements in the stability results, especially when working with…

Let $H^{\varepsilon}=-\frac{d^2}{dx^2}+\varepsilon x +V$, $\varepsilon\geq0$, on $L^2(\mathbf{R})$. Let $V=\sum_{k=1}^Nc_k|\psi_k\rangle\langle\psi_k|$ be a rank $N$ operator, where the $\psi_k\in L^2(\mathbf{R})$ are real, compactly…

We analyze the stability of the Einstein static universe by considering homogeneous scalar perturbations in the context of f(R) modified theories of gravity. By considering specific forms of f(R), the stability regions of the solutions are…