相关论文: Locally optimal Functional Quantization
A standard task in solid state physics and quantum chemistry is the computation of localized molecular orbitals known as Wannier functions. In this manuscript, we propose a new procedure for computing Wannier functions in one-dimensional…
We study the linear polarization constants of finite dimensional Banach spaces. We obtain the correct asymptotic behaviour of these constants for the spaces $\ell_p^d$: they behave as $\sqrt[p]{d}$ if $1\le p\le 2$ and as $\sqrt{d}$ if…
Maximally localized Wannier functions are the key tool for a variety of physical applications of Bloch states. Here we develop a simple and exact procedure to construct maximally localized Wannier functions for one dimensional periodic…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
We give a local characterization of the class of functions having positive distributional derivative with respect to $\bar{z}$ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild non-degeneracy…
We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…
We discuss a method for determining the optimally-localized set of generalized Wannier functions associated with a set of Bloch bands in a crystalline solid. By ``generalized Wannier functions'' we mean a set of localized orthonormal…
The semilinear space-time fractional Schr\"odinger equation is considered. First, we give the explicit form for the fundamental solutions by using the Fox $H$-functions in order to to establish some $L^s$ decay estimates. After that, we…
We investigate uniform, strong, weak and almost weak stability of multiplication semigroups on Banach space valued $L^p$-spaces. We show that, under certain conditions, these properties can be characterized by analogous ones of the…
We consider the design of systems for sequential decentralized detection, a problem that entails several interdependent choices: the choice of a stopping rule (specifying the sample size), a global decision function (a choice between two…
We study a local version of the ball-covering problem in Banach spaces, and obtain a complete solution to it in terms of the norm derivatives. We illustrate the advantage of the local approach by obtaining substantial refinements of several…
Usually, for extension of local maps, one uses multiplication by so called bump functions. However, majority of infinite-dimensional linear topological spaces do not have smooth bump functions. Therefore, in \cite{BR} we suggested a new…
We prove a generalised Yuan--Hunt--Ma\~n\'e Conjecture: if $\mathcal{F}$ is the Banach space of $\alpha$-H\"older functions, and $\mathcal{T}$ is either a space of Lipschitz expanding maps, or of Anosov diffeomorphisms, or the family of…
The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We…
We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$. These functionals, in many cases, are associated…
Let $X, Y$ be two independent identically distributed (i.i.d.) random variables taking values from a separable Banach space $(\mathcal{X}, \|\cdot\|)$. Given two measurable subsets $F, K\subseteq\cal{X}$, we established distribution free…
In this paper we introduce a class of Banach spaces of functions of class C^r (where r is a positive real number) and the associated dual spaces of distributions of order r, which turn out to be useful in p-adic Langlands theory. We…
We study differentiability properties of convex operators defined on a Banach space with values in an $\Lc_p$ space and of their compositions with monotonic convex functionals on this space. We develop new tools for operators enjoying an…
An important consequence of the Hahn-Banach Theorem says that on any locally convex Hausdorff topological space $X$, there are sufficiently many continuous linear functionals to separate points of $X$. In the paper, we establish a `local'…
While it is well known that nonlinear methods of approximation can often perform dramatically better than linear methods, there are still questions on how to measure the optimal performance possible for such methods. This paper studies…