相关论文: Full characterizations of the variational McShane …

Let $[a,b] $ be an interval in $\mathbb{R}$ and let $F$ be a real valued function defined at the endpoints of $[a,b]$ and with a certain number of discontinuities within $[a,b] $. Having assumed $F$ to be differentiable on a set $[a,b]…

It is shown here that if $(Y,\|\cdot\|_Y)$ is a Banach space in which martingale differences are unconditional (a UMD Banach space) then there exists $c=c(Y)\in (0,\infty)$ with the following property. For every $n\in \mathbb{N}$ and…

We consider the space of real-valued continuously differentiable functions on a compact subset of a euclidean space. We characterize the completeness of this space and prove that the space of restrictions of continuously differentiable…

We introduce a family of Banach spaces of measures, each containing the set of measures with density of bounded variation. These spaces are suitable for the study of weighted transfer operators of piecewise-smooth maps of the interval where…

Using the notion of complete compactness introduced by H. Saar, we define completely almost periodic functionals on completely contractive Banach algebras. We show that, if $(M,\Gamma)$ is a Hopf--von Neumann algebra with $M$ injective,…

We first introduce the arithmetic subderivative of a positive integer with respect to a non-empty set of primes. This notion generalizes the concepts of the arithmetic derivative and arithmetic partial derivative. More generally, we then…

For set-valued functions (SVFs, multifunctions), mapping a compact interval $[a,b]$ into the space of compact non-empty subsets of ${\mathbb R}^d$, we study approximation based on the metric approach that includes metric linear…

Let $\mathcal{A}$ denote the class of analytic functions $f$ on the unit disc $\mathbb{D}=\{z\in\mathbb{C}:\;|z|<1\}$ normalized by $f(0)=0$ and $f^{\prime}(0)=1$. In the present article, we consider and $\mathcal{F}(c)$ the subclasses of…

In this paper, we introduce and analyze multidimensional vector-valued Laplace transform of functions with values in sequentially complete locally convex spaces. A great number of our results seem to be new even for the functions with…

This paper demonstrates that the space of piecewise smooth functions can be well approximated by the space of functions defined by a set of simple (non-linear) operations on smooth uniform splines. The examples include bivariate functions…

The notion of adequate function has been recently introduced in order to characterize the essentially strictly functions on a reflexive Banach space among the weakly lower semicontinuous ones. In this paper we reinforce this concept and…

We introduce a family of variational functionals for spinor fields on a compact Riemann surface $M$ that can be used to find close-to-conformal immersions of $M$ into $\mathbb{R}^3$ in a prescribed regular homotopy class. Numerical…

We study Henstock-type integrals for functions defined in a Radon measure space and taking values in a Banach lattice $X$. Both the single-valued case and the multivalued one are considered (in the last case mainly $cwk(X)$-valued mappings…

We prove that a locally integrable function $f:(a,b) \to \mathbb R$ must be affine if its mean oscillation, considered as a function of intervals, can be extended to a locally finite Borel measure. In particular, we show that any function…

Conditional Monte Carlo or pre-integration is a powerful tool for reducing variance and improving the regularity of integrands when using Monte Carlo and quasi-Monte Carlo (QMC) methods. To select the variable to pre-integrate, one must…

Let $\phi$ be a psh function on a bounded pseudoconvex open set $\Omega \subset \C^n$, and let ${\cal I}(\phi)$ be the associated multiplier ideal sheaf. Motivated by resolution of singularities issues, we establish an effective version of…

Let $I\subseteq{\mathbb{R_+}}$ be a non empty and non singleton interval where ${\mathbb{R_+}}$ denotes the set of all non negative numbers. A function $\Phi: I\to {\mathbb{R_+}}$ is said to be subadditive if for any $x,y$ and $x+y\in I$,…

Inferential models (IMs) offer provably reliable, data-driven, possibilistic statistical inference. But despite the IM framework's theoretical and foundational advantages, efficient computation is a challenge. This paper presents a simple…

The aim of this note is to characterize all pairs of sufficiently smooth functions for which the mean value in the Cauchy Mean Value Theorem is taken at a point which has a well-determined position in the interval. As an application of this…

Tame functions are a class of nonsmooth, nonconvex functions, which feature in a wide range of applications: functions encountered in the training of deep neural networks with all common activations, value functions of mixed-integer…