Characterizations of the Saito-Kurokawa lifting: a survey

There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular forms to Siegel modular forms of degree 2. In addition to giving a survey of known characterizations, we apply a recent result of Weissauer to provide a number of new and simpler characterizations of Saito-Kurokawa lifts

Characterizations of derivations

The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations. In Chapter 2 we collect all the definitions and results regarding derivations that are essential while studying this area. In Chapter 3 we intend to show that derivations can be characterized by one single functional equation. More exactly, we study here the following problem. Let $Q$ be a commutative ring and let $P$ be a subring of $Q$. Let $\lambda, \mu\in Q\setminus\left\{0\right\}$ be arbitrary, $f\colon P\rightarrow Q$ be a function and consider the equation $$\lambda\left[f(x+y)-f(x)-f(y)\right]+ \mu\left[f(xy)-xf(y)-yf(x)\right]=0 \quad \left(x, y\in P\right).$$ In this chapter it will be proved that under some assumptions on the rings $P$ and $Q$, derivations can be characterized via the above equation. Chapter 4 is devoted to the additive solvability of a system of functional equations. Moreover, the linear dependence and independence of the additive solutions $d_{0},d_{1},\dots,d_{n} \colon\mathbb{R}\to\mathbb{R}$ of the above system of equations is characterized. Finally, the closing chapter deals with the following problem. Assume that $\xi\colon \mathbb{R}\to \mathbb{R}$ is a given differentiable function and for the additive function $f\colon \mathbb{R}\to \mathbb{R}$, the mapping $$\varphi(x)=f\left(\xi(x)\right)-\xi'(x)f(x)$$ fulfills some regularity condition on its domain. Is it true that in such a case $f$ is a sum of a derivation and a linear function

Metric characterizations II

The present paper is a sequel to our paper "Metric characterization of isometries and of unital operator spaces and systems". We characterize certain common objects in the theory of operator spaces (unitaries, unital operator spaces, operator systems, operator algebras, and so on), in terms which are purely linear-metric, by which we mean that they only use the vector space structure of the space and its matrix norms. In the last part we give some characterizations of operator algebras (which are not linear-metric in our strict sense described in the paper).Comment: Presented at the AMS/SAMS Satellite Conference on Abstract Analysis, University of Pretoria, South Africa, 5-7 December 2011. Revision of 2/24/2012 (Examples after theorem 3.2 added

A class of infinite convex geometries

Various characterizations of finite convex geometries are well known. This note provides similar characterizations for possibly infinite convex geometries whose lattice of closed sets is strongly coatomic and lower continuous. Some classes of examples of such convex geometries are given.Comment: 10 page

Characterizations of Distributions via Conditional Expectation of Generalized Order Statistics

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics

Axioms for consensus functions on the n-cube

An elementary general result is proved that allows for simple characterizations of well-known location/consensus functions (median, mean and center) on the n-cube. In addition, alternate new characterizations are given for the median and anti-median functions on the n-cube.Comment: 12 page

Various Characterizations of Modified Weibull and Log Modified Distributions

Various characterizations of the well-known modifiedWeibull and log-modifiedWeibull distributions are presented. These characterizations are based on a simple relationship between two truncated moments; on the hazard function and on functions of the order statistics