Related papers: Global Inversion of Functions: an Introduction

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

We extend the theory of distributional kernel operators to a framework of generalized functions, in which they are replaced by integral kernel operators. Moreover, in contrast to the distributional case, we show that these generalized…

The problem of finding out the global minimum of a multiextremal functional is discussed. One frequently faces with such a functional in various applications. We propose a procedure, which depends on the dimensionality of the problem…

The Fock transform recently introduced by the authors in a previous paper is applied to investigate convergence of generalized functional sequences of a discrete-time normal martingale $M$. A necessary and sufficient condition in terms of…

Fourier transforms are ubiquitous mathematical tools in basic and applied sciences. We here report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform. In the…

This is an introduction to calculus, and its applications to basic questions from physics. We first discuss the theory of functions $f:\mathbb R\to\mathbb R$, with the notion of continuity, and the construction of the derivative $f'(x)$ and…

This work considers the algebras of functions in the quantum matrix ball. An explicit formula for a positive invariant integral is presented.

A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.

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…

This article is meant as a summary and introduction to the ideas of effective field theory as applied to gravitational systems. Contents: 1. Introduction 2. Effective Field Theories 3. Low-Energy Quantum Gravity 4. Explicit Quantum…

In this paper we aim to generalize results obtained in the framework of fractional calculus by the way of reformulating them in terms of operator theory. In its own turn, the achieved generalization allows us to spread the obtained…

We introduce a self-inverse function via an integral equivalent to a two-term combination of dilogarithms. We refer to this function as a fundamental form, since there is a family of extensions of this function that satisfy similar…

The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…

This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…

Although inverse limits with factor spaces indexed by the positive integers are most commonly studied, Ingram and Mahavier have defined inverse limits with set-valued functions broadly enough for any directed index set to be used. In this…

The paper is devoted to the introduction of natural deduction systems for some weak subintuitionistic logics, along with proofs of normalization theorems for these systems.

The problem of inverting a system in presence of a series-defined output is analyzed. Inverse models are derived that consist of a set of algebraic equations. The inversion is performed explicitly for an output trajectory functional, which…

In this paper we start a classification of certain global integrals. First, we use the language of unipotent orbits to write down a family of global integrals. We then classify all those integrals which satisfy the dimension equation we…

A general divergence measure for monotonic functions is introduced. Its connections with the f-divergence for convex functions are explored. The main properties are pointed out.

Generalized inverses of tensors play increasingly important roles in computational mathematics and numerical analysis. It is appropriate to develop the theory of generalized inverses of tensors within the algebraic structure of a ring. In…