Related papers: Characterization of test functions in CKS-space
We study the localization properties of generalized functions defined on a broad class of spaces of entire analytic test functions. This class, which includes all Gelfand--Shilov spaces $S^\beta_\alpha(\R^k)$ with $\beta<1$, provides a…
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
We consider a one-dimensional discrete-space birth process with a bounded number of particle per site. Under the assumptions of the finite range of interaction, translation invariance, and non-degeneracy, we prove a shape theorem. We also…
In this paper we offer a complete methodology for sufficient dimension reduction called the test function (TF). TF provides a new family of methods for the estimation of the central subspace (CS) based on the introduction of a nonlinear…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
The characteristic functional is the infinite-dimensional generalization of the Fourier transform for measures on function spaces. It characterizes the statistical law of the associated stochastic process in the same way as a characteristic…
The main purpose of this paper is to investigate the stability problem of some functional equations that appear in the characterization problem of information measures.
In this article we explore under which conditions on the interior function the composition of functions is measurable. We also study the sharpness of the result by providing a counterexample for weaker hypotheses.
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion.
We examine the question of which characteristic functions yield Weyl-Heisenberg frames for various values of the parameters. We also give numerous applications of frames of characteristic functions to the general case (g,a,b).
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
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…
Test functions are important to validate new optimization algorithms and to compare the performance of various algorithms. There are many test functions in the literature, but there is no standard list or set of test functions one has to…
A topological space $X$ is Baire if the Baire Category Theorem holds for $X$, i.e., the intersection of any sequence of open dense subsets of $X$ is dense in $X$. One of the interesting problems in the theory of functional spaces is the…
We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.
This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.
We extend a theorem by Kleiner, stating that on a group with polynomial growth, the space of harmonic functions of polynomial of at most $k$ is finite dimensional, to the settings of locally compact groups equipped with measures with…
We establish a functional central limit theorem for Ripley's K-function for two classes of point processes. One is the class of point processes having exponential decay of correlations and further satisfying a conditional m-dependence…
The purpose of testing a system with respect to a requirement is to refute the hypothesis that the system satisfies the requirement. We build a theory of tests and refutation based on the elementary notions of satisfaction and refinement.…
The purpose of this paper is to find the characterization of the Sheffer polynomial sets satisfying the d-orthogonality conditions. The generating function form of these polynomial sets is given in Theorem 2.2. As applications of the…