Related papers: BMO-type functionals, total variation, and $\Gamma…

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms $G_p: T_pM \to [0,\infty]$ are given. When we consider sub-Riemannian manifolds, our definition coincide with…

In the setting of a metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we define and study a class of BV functions with zero boundary values. In particular, we show that the class is the closure of…

We consider the approximation of the total variation of a function by the family of non-local and non-convex functionals introduced by H. Brezis and H.-M. Nguyen in a recent paper. The approximating functionals are defined through double…

We prove a local version of Fefferman-Stein inequality for the local sharp maximal function, and a local version of John-Nirenberg inequality for locally BMO functions, in the framework of locally homogeneous spaces, in the sense of…

Let $F_{BC}(\lambda,k;t)$ be the Heckman-Opdam hypergeometric function of type BC with multiplicities $k=(k_1,k_2,k_3)$ and weighted half sum $\rho(k)$ of positive roots. We prove that $F_{BC}(\lambda+\rho(k),k;t)$ converges for…

Completely multiplicative functions whose sum is zero ($CMO$).The paper deals with $CMO$, meaning completely multiplicative ($CM$) functions $f$ such that $f(1)=1$ and $\sum\limits\_1^\infty f(n)=0$. $CM$ means $f(ab)=f(a)f(b)$ for all…

Let $\mathbb{F}\subset \mathbb{K}$ be fields with characteristic zero, $n$ be a positive integer and $\kappa\in \mathbb{K}$. In this paper, we determine those monomials $f\colon \mathbb{F}\to \mathbb{K}$ of degree $n$ for which \[ f(x^{2})=…

We consider various notions of vanishing mean oscillation on a (possibly unbounded) domain $\Omega \subset \mathbb{R}^n$, and prove an analogue of Sarason's theorem, giving sufficient conditions for the density of bounded Lipschitz…

Let $\Gamma$ be a crystal group in $\mathbb R^d$. A function $\varphi:\mathbb R^d\longrightarrow \mathbb C$ is said to be {\em crystal-refinable} (or $\Gamma-$refinable) if it is a linear combination of finitely many of the rescaled and…

For background geometries whose metric contain a scale $\gamma$ we reformulate the Born-Infeld D-brane action in terms of $\epsilon \equiv \gamma /(2\pi \alpha ')$. This may be taken as a starting point for various perturbative treatments…

In these notes, uniform convergence on compacta is studied on the space of functions taking values in the set of finite Borel measures. Related limit theorems, including L\'evy's continuity theorem and functional limit theorems for…

Motivated by applications to image reconstruction, in this paper we analyse a \emph{finite-difference discretisation} of the Ambrosio-Tortorelli functional. Denoted by $\varepsilon$ the elliptic-approximation parameter and by $\delta$ the…

We prove a lower semicontinuity result for a functional of linear growth initially defined by \[ \int_{\Omega}F\left(\frac{dDu}{d\mu}\right)\,d\mu \] for $u\in BV(\Omega;\mathbb{R}^N)$ with $Du\ll \mu$. The positive Radon measure $\mu$ is…

Let $\Omega$ be a bounded pseudoconvex domain in $\mathbb{C}^n$, and let $\phi$ be a strictly plurisubharmonic function on $\Omega$. For each $k\in\mathbb{N}$, we consider determinantal point process $\Lambda_k$ with kernel $K_{k\phi}$,…

Let $X$ be a Banach space, let $(\Omega,\mu)$ be a $\sigma$-finite measure space and let $A,B\colon\Omega\to B(X)$ be strongly measurable $\gamma$-bounded functions. We show that for all $x\in X$ and all $x^*\in X^*$, there exist a Hilbert…

Let $\kappa\in(4,8)$. Let $\gamma$ be an SLE$_\kappa$ curve in a Jordan domain $D$ connecting $a_1\ne a_2\in\partial D$. We attach $\gamma$ with two open boundary arcs $A_1,A_2$ of $D$, which share end points $b_1\ne b_2\in\partial…

The growth index $\gamma$ is a powerful trigger for detecting deviations from $\Lambda$CDM. However, its value is often determined by considering an asymptotic constant value that works for all redshift, or else following a chosen…

We study a discrete-to-continuous Gamma-limit of a family of high-contrast double porosity type functionals defined on a scaled integer lattice. Under periodicity and p-growth conditions we prove the homogenization result and describe the…

We prove a homogenization theorem for a class of quadratic convolution energies with random coefficients. Under suitably stated hypotheses of ergodicity and stationarity we prove that the $\Gamma$-limit of such energy is almost surely a…

Let $\mathcal{U(\alpha, \lambda)}$, $0<\alpha <1$, $0 < \lambda <1$ be the class of functions $f(z)=z+a_{2}z^{2}+a_{3}z^{3}+\cdots$ satisfying $$\left|\left(\frac{z}{f(z)}\right)^{1+\alpha}f'(z)-1\right|<\lambda$$ in the unit disc ${\mathbb…