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The notion of a shift-compact set in an abelian topological group $X$ plays a significant role in functional equations and inequalities, especially so since each Borel set that is not Haar-meagre, alternatively not Haar-null, is necessarily…

Classical Analysis and ODEs · Mathematics 2019-12-23 N. H. Bingham , Eliza Jablonska , Wojciech Jablonski , Adam J. Ostaszewski

This paper concerns a variational representation formula for Wiener functionals. Let $B=\{ B_{t}\} _{t\ge 0}$ be a standard $d$-dimensional Brownian motion. Bou\'e and Dupuis (1998) showed that, for any bounded measurable functional $F(B)$…

Probability · Mathematics 2022-03-08 Yuu Hariya , Sou Watanabe

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over bounded volumes that have smooth boundaries in three dimensions is described. A key aspect of this approach is that it…

Numerical Analysis · Mathematics 2023-01-11 Jonah A. Reeger

Avikainen showed that, for any $p,q \in [1,\infty)$, and any function $f$ of bounded variation in $\mathbb{R}$, it holds that $\mathbb{E}[|f(X)-f(\widehat{X})|^{q}] \leq C(p,q) \mathbb{E}[|X-\widehat{X}|^{p}]^{\frac{1}{p+1}}$, where $X$ is…

Probability · Mathematics 2020-11-30 Dai Taguchi , Akihiro Tanaka , Tomooki Yuasa

Let $X$ be a smooth compact manifold and $v$ a vector field on $X$ which admits a smooth function $f: X \to \mathbf R$ such that $df(v) > 0$. Let $\partial X$ be the boundary of $X$. We denote by $C^\infty(X)$ the algebra of smooth…

Geometric Topology · Mathematics 2023-03-02 Gabriel Katz

Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \leq -1$, and let $\partial X$ denote the boundary at infinity of $X$. Let $h > 0$ denote the mean curvature of horospheres in $X$, and…

Differential Geometry · Mathematics 2018-02-22 Kingshook Biswas

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

Functional Analysis · Mathematics 2025-12-18 Vladimir Müller , Yuri Tomilov

We extend the Matom\"{a}ki-Radziwi\l\l{} theorem to a large collection of unbounded multiplicative functions that are uniformly bounded, but not necessarily bounded by 1, on the primes. Our result allows us to estimate averages of such a…

Number Theory · Mathematics 2021-11-15 Alexander P. Mangerel

We derive Berry-Esseen approximation bounds for general functionals of independent random variables, based on chaos expansions methods. Our results apply to $U$-statistics satisfying the weak assumption of decomposability in the Hoeffding…

Probability · Mathematics 2020-10-12 Nicolas Privault , Grzegorz Serafin

The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…

Classical Analysis and ODEs · Mathematics 2026-01-26 Erik Talvila

We prove a Lusin approximation of functions of bounded variation. If $f$ is a function of bounded variation on an open set $\Omega\subset X$, where $X=(X,d,\mu)$ is a given complete doubling metric measure space supporting a $1$-Poincar\'e…

Functional Analysis · Mathematics 2025-01-14 Panu Lahti , Khanh Nguyen

We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…

Statistics Theory · Mathematics 2011-11-10 Vladas Pipiras , Murad S. Taqqu , Patrice Abry

We describe a method for calculating action-angle variables in axisymmetric galactic potentials using Birkhoff normalization, a technique from Hamiltonian perturbation theory. An advantageous feature of this method is that it yields…

Astrophysics of Galaxies · Physics 2024-04-29 Sam Hadden

We analyze some properties of the measures in the dual of the space $BV$, by considering (signed) Radon measures satisfying a perimeter bound condition, which means that the absolute value of the measure of a set is controlled by the…

Analysis of PDEs · Mathematics 2025-01-09 Giovanni E. Comi , Gian Paolo Leonardi

We introduce a family of (nonlinear) pairing measures that ensure the validity of the divergence rule for composite functions $\boldsymbol{B}(x,u(x))$, where $\boldsymbol{B}(\cdot,t)$ is a bounded divergence-measure vector field, and $u$ is…

Functional Analysis · Mathematics 2026-04-16 Graziano Crasta , Virginia De Cicco , Annalisa Malusa

We consider a $U(1)$ Maxwell-Chern-Simons theory in $5$-dimensions, and analyze the vector perturbations around a classical charged black-brane background. We solve the equations of motion for these perturbations in a derivative expansion.…

High Energy Physics - Theory · Physics 2022-08-11 Jewel K. Ghosh , M. Arshad Momen

For a projective variety X defined over a field K, there is a special class of self-morphisms of X called algebraic dynamical systems. In this paper we take K to be the function field of a smooth curve and prove that at each place of K,…

Number Theory · Mathematics 2015-05-13 X. W. C. Faber

In this paper we describe all rotation $H$-hypersurfaces in $H^n \times R$ and use them as barriers to prove existence and characterization of certain vertical $H$-graphs and to give symmetry and uniqueness results for compact…

Differential Geometry · Mathematics 2019-10-07 Pierre Bérard , Ricardo Sa Earp

In this paper, we study the shift on the space of uniformly bounded continuous functions band-limited in a given compact interval with the standard topology of tempered distributions. We give a constructive proof of the existence of minimal…

Dynamical Systems · Mathematics 2022-04-11 Jianjie Zhao

We introduce and study spaces of multivariate functions of bounded variation generalizing the classical Jordan and Wiener spaces. Multivariate generalizations of the Jordan space were given by several prominent researchers but each of them…

Functional Analysis · Mathematics 2018-11-20 A. Brudnyi , Yu. Brudnyi
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