Related papers: Local spectral estimates and quantitative weak mix…

We experimentally determine weak values for a single photon's polarization, obtained via a weak measurement that employs a two-photon entangling operation, and postselection. The weak values cannot be explained by a semiclassical wave…

In this paper, we consider entropy spectra on topological Markov shifts. We prove that if two measure-preserving dynamical systems of Gibbs measures with H\"older continuous potentials are isomorphic, then their entropy spectra are the…

We investigate limit theorems for Birkhoff sums of locally H\"older functions under the iteration of Gibbs-Markov maps. Aaronson and Denker have given sufficient conditions to have limit theorems in this setting. We show that these…

For fractional wave equations with low H\"older regularity damping, we establish quantitative energy decay rates for their solutions when the geometric control condition holds. The energy decay rates depend explicitly on the H\"older…

In this paper, we consider the problem of approximating the spectral distribution for a class of random operators over sofic groups. For this purpose, we make use of the concept of locally and empirically converging measures defined by…

We look at invariance of a.e. boundary condition spectral behavior under perturbations, $W$, of half-line, continuum or discrete Schr\"odinger operators. We extend the results of del Rio, Simon, Stolz from compactly supported $W$'s to…

Let $G$ be a locally compact group and $\mu$ a probability measure on $G,$ which is not assumed to be absolutely continuous with respect to Haar measure. Given a unitary representation $(\pi, \cal H)$ of $G,$ we study spectral properties of…

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs…

For a general group G we consider various weak mixing properties of nonsingular actions. In the case where the action is actually measure preserving all these properties coincide, and our purpose here is to check which implications persist…

We consider primitive aperiodic substitutions of constant length q and prove that, in order to have a Lebesgue component in the spectrum of the associated dynamical system, it is necessary that one of the eigenvalues of the substitution…

In this paper, we present local H\"older estimates for the degenerate Keller-Segel system \eqref{eq-cases-aligned-main-problem-of-Keller-Segel-System} below in the range of $m>1$ and $q>1$ before a blow-up of solutions. To deal with…

We prove local boundedness, Harnack's inequality and local regularity for weak solutions of quasilinear degenerate elliptic equations in divergence form with Rough coefficients. Degeneracy is encoded by a non-negative, symmetric, measurable…

A regularity lemma for polynomials provides a decomposition in terms of a bounded number of approximately independent polynomials. Such regularity lemmas play an important role in numerous results, yet suffer from the familiar shortcoming…

We consider a class of nonlinear integro-differential equations whose leading operator is obtained as a superposition of $(-\Delta_{p})^{s}$ and $(-\Delta_{p})^{t}$, where $0<s<t<1<p<\infty$, weighted via two possibly degenerate…

Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement.…

We establish local boundedness and local H\"older continuity of weak solutions to the following prototype problem: $$ -\operatorname{div}\left(|x|^{-2 \beta}|\nabla u|^{\mathbf{q}-2} \nabla u\right)+(-\Delta)_{p(\cdot, \cdot),…

This article proves the existence, non-existence, regularity and asymptotic behavior of weak solutions for a class of mixed local-nonlocal parabolic problems involving singular nonlinearities and measure data extending the works of…

We prove global H\"older regularity result for weak solutions $u\in N^{1,p}(\Omega, \mu)$ to a PDE of $p$-Laplacian type with a measure as non-homogeneous term: \[ -\text{div}\!\left( |\nabla u|^{p-2}\nabla u \right)=\overline\nu, \] where…

A new technique based on H\"older's integral inequality is applied to QCD sum-rules to provide fundamental constraints on the sum-rule parameters. These constraints must be satisfied if the sum-rules are to consistently describe integrated…

A method is developed for analysing asymptotic behaviour of terms involving an arbitrary integer order powers of L p functions by means of H-measures. It is applied to the small amplitude homogenisation problem for a stationary diffusion…