Related papers: Fundamental function for Grand Lebesgue Spaces
In this paper, we give a generate function for the $\sigma_1$ function. Then we find some connections between the $\sigma_1$ function and the Ramanujan's tau function. We hope this connection will give some insights into the unsolved…
We solve general 1-matrix models without taking the double scaling limit. A method of computing generating functions is presented. We calculate the generating functions for a simple and double torus. Our method is also applicable to more…
Density Functional Theory relies on universal functionals characteristic of a given system. Those functionals in general are different for the electron gas and for jellium (electron gas with uniform background). However, jellium is…
In the paper we consider a realization of a finite dimensional irreducible representation of the Lie algebra $\mathfrak{gl}_n$ in the space of functions on the group $GL_n$. It is proved that functions corresponding to Gelfand-Tsetlin…
Gel'fand triples of test and generalized functionals in Gaussian spaces are constructed and characterized.
In this work, we will generalize the moment generating function to Riesz spaces. We will derive some of its properties and use it to prove concentration inequalities on Riesz spaces.
We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces $L_{P}$ built from index functions $P\colon\Omega\to(0,\infty]$ on $\sigma$-finite measure spaces $(\Omega,\Sigma,\mu)$. Specifically, we prove that if…
In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
This text grew out of notes I have used in teaching a one quarter course on integration at the advanced undergraduate level. My intent is to introduce the Lebesgue integral in a quick, and hopefully painless, way and then go on to…
The main objective of this paper is to provide a comprehensive demonstration of recent results regarding the structures of the weighted Ces\`aro and Copson function spaces. These spaces' definitions involve local and global weighted…
We study the concept of a code (or shift) space for a generalized iterated function system (GIFS in short). We prove that relations between GIFSs and their code spaces are analogous to the case of classical IFSs. As an application, we…
Modelling of singularities given by discontinuous functions or distributions by means of generalized functions has proved useful in many problems posed by physical phenomena. We introduce in a systematic way generalized functions of…
In this note some structural properties of grand variable exponent Lebesgue/ Morrey spaces over spaces of homogeneous type are obtained. In particular, it is proved that the closure of the class of bounded functions and the closure of…
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency…
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
The explicit expressions for the non-singlet DIS structure function g_1 at small $x$ are obtained by resumming the leading logarithmic contributions. The role played by the fits for the initial parton densities currently used in the DGLAP…
Sequences are often conveniently encoded in the form of a generating function depending on a formal variable. This note presents two observations that allow one to draw conclusions about the generated sequence from the generating function.…
A simple but rigorous proof of the Fundamental Theorem of Calculus is given in geometric calculus, after the basis for this theory in geometric algebra has been explained. Various classical examples of this theorem, such as the Green's and…
In this article we find some sufficient conditions for the set in the Bilateral Grand Lebesgue Space to be compact set. We consider applications into numerical methods and in the basis problem.