Related papers: Note on a result of Kerman and Weit
Freiman's $3k-4$ Theorem states that if a subset $A$ of $k$ integers has a Minkowski sum $A+A$ of size at most $3k-4$, then it must be contained in a short arithmetic progression. We prove a function field analogue that is also a…
A classical result states that every lower bounded superharmonic function on $\Bbb R^2$ is constant. In this paper the following (stronger) one-circle version is proven. If $f\colon \Bbb R^2\to (-\infty,\infty]$ is lower semicontinuous,…
In this short paper, we shall provide a dynamical systems' proof of the famous Kraft-McMillan inequality and its converse. Kraft-McMillan inequality is a basic result in information theory which gives a necessary and sufficient condition…
An effective force induced by spatially depending decoherence is predicted. The phenomenon is illustrated by a simple model of a 1/2-spin particle subjected to distributed unselective measurement of noncommuting spin components.
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
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…
In this paper we present a combinatorial proof of the Kronecker--Weber Theorem for global fields of positive characteristic. The main tools are the use of Witt vectors and their arithmetic developed by H. L. Schmid. The key result is to…
A functional analog of the Klain-Schneider theorem for vector-valued valuations on convex functions is established, providing a classification of continuous, translation covariant, simple valuations. Under additional rotation equivariance…
We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{\alpha, q, a}^{2}$-functions whose q-Weinstein…
Hadwiger's Theorem states that Euclidean-invariant convex-continuous valuations of definable sets are linear combinations of intrinsic volumes. We lift this result from sets to data distributions over sets, specifically, to definable…
There exists a function f: N -> N such that for every positive integer d, every quasi-finite field K and every projective hypersurface X of degree d and dimension at least f(d), the set X(K) is non-empty. This is a special case of a more…
Regular variation is a continuous-parameter theory; we work in a general setting, containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. We give sequential versions of the main theorems, that is,…
We study very smooth functions on the real line, namely Schwartz functions, that satisfy a finite identity relating their translates and a single modulation. Concretely, we assume there is a nontrivial linear combination of translates of…
It is shown that each continuous even Minkowski valuation on convex bodies of degree $1 \leq i \leq n - 1$ intertwining rigid motions is obtained from convolution of the $i$th projection function with a unique spherical Crofton…
It is developed the theory of the Dirichlet problem for harmonic functions. On this basis, for the nondegenerate Beltrami equations in the quasidisks and, in particular, in the smooth domains, it is proved the existence of regular solutions…
The axiomatic approach based on Wightman functions is developed in noncommutative quantum field theory. We have proved that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
This paper presents a spectral calculus for computing the spectrum of a causal Lorentz invariant Borel complex measure on Minkowski space, thereby enabling one to compute the density for such a measure with respect to Lebesque measure. It…
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
Let $\cD$ be the Dirichlet space, namely the space of holomorphic functions on the unit disk whose derivative is square-integrable. We establish a new sufficient condition for a function $f\in\cD$ to be {\em cyclic}, i.e. for $\{pf:…
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the…