Related papers: Semicontinuity of the spectrum at infinity

Integrable Hamiltonian systems on almost-symplectic manifolds have recently drawn some attention. Under suitable properties, they have a structure analogous to those of standard symplectic-Hamiltonian completely integrable systems. Here we…

We define the half-volume spectrum $\{\tilde \omega_p\}_{p\in \mathbb N}$ of a closed manifold $(M^{n+1},g)$. This is analogous to the usual volume spectrum of $M$, except that we restrict to $p$-sweepouts whose slices each enclose half the…

We define and prove some properties of the semi-classical wavefront set. We also define and study semi-classical Fourier integral operators, of which we give a complete characterization. Lastly, we prove a generalization of the…

In this work, we present basic results and applications of Stepanov pseudo almost periodic functions with measures. Using only the continuity assumption, we prove a new composition result of $\mu$-pseudo almost periodic functions in…

In this paper we discuss the notion of universality for classes of candidate common Lyapunov functions of linear switched systems. On the one hand, we prove that a family of absolutely homogeneous functions is universal as soon as it…

We study the asymptotic complexity constant of the sequence of approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal $K$. We show how full symmetry implies existence of the asymptotic complexity…

We show that a spectrum of frequencies obtained by a random perturbation of the integers allows one to represent any measurable function on R by an almost everywhere converging sum of harmonics almost surely.

We prove boundedness and regularity estimates for weak solutions to a class of linear nonlocal equations involving integro-differential operators with almost no order of differentiability. In particular, we show that bounded weak solutions…

We show that the number of parameters for CM-modules of prescribed rank is semi-continuous in families of CM rings of Krull dimension 1. This transfers a result of Knoerrer from the commutative to the not necessarily commutative case. For…

We prove several new results on the absolutely continuous spectra of perturbed one-dimensional Stark operators. First, we find new classes of perturbations, characterized mainly by smoothness conditions, which preserve purely absolutely…

The problem we are considering came up in connection with the classification of singularities in positive characteristic. Then it is important that certain invariants like the determinacy can be bounded simultaneously in families of formal…

In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show,…

We recall the definition of quasinearly subharmonic functions, point out that this function class includes, among others, subharmonic functions, quasisubharmonic functions, nearly subharmonic functions and essentially almost subharmonic…

We conduct the multifractal analysis of self-affine measures for "almost all" family of affine maps. Besides partially extending Falconer's formula of $L^q$-spectrum outside the range $1< q\leq 2$, the multifractal formalism is also…

In this paper, we introduce a new notion of convergence for the Laplace eigenfunctions in the semiclassical limit, the local weak convergence. This allows us to give a rigorous statement of Berry's random wave conjecture. Using recent…

This paper is dedicated to the unique continuation properties of the solutions to nonlinear variational problems. Our analysis covers the case of nonlinear autonomous functionals depending on the gradient, as well as more general double…

Given a strictly positive measure, we characterize inner semicontinuous solid convex-valued mappings for which continuous functions which are selections almost everywhere are selections. This class contains continuous mappings as well as…

It is stated equicontinuity and normality of families $\frak{F}^{\Phi}$ of the so--called homeomorphisms with finite distortion on conditions that $K_{f}(z)$ has finite mean oscillation, singularities of logarithmic type or integral…

Within the framework of balayage spaces (the analytical equivalent of nice Hunt processes), we prove equicontinuity of bounded families of harmonic functions and apply it to obtain criteria for compactness of potential kernels.

We show that the non-centered maximal function of a BV function is quasicontinuous. We also show that \emph{if} the non-centered maximal functions of an SBV function is a BV function, then it is in fact a Sobolev function. Using a recent…