Related papers: Functional Analysis
In this paper we consider Idempotent Functional Analysis, an `abstract' version of Idempotent Analysis developed by V. P. Maslov and his collaborators. We give a review of the basic ideas of Idempotent Analysis. The correspondence between…
Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the…
Quantum harmonic analysis extends classical harmonic analysis by integrating quantum mechanical observables, replacing functions with operators and classical convolution structures with their noncommutative counterparts. This paper explores…
In this paper, a functional model of interactions in quantum theory (QT) is proposed. A functional model describes the dynamic evolution of a physical system in terms of process steps and intermediate states. That is, it describes how…
Dimensional analysis is a simple qualitative method for determining essential connections between physical quantities. It is applicable to a multitude of physics problems, many of which canbe introduced early on in a university physics…
This paper is a continuation of the paper (A.G.Ramm, Amer. Math. Monthly, 108, N 9, (2001), 855-860), where bounded Fredholm operators are studied. The theory of bounded linear Fredholm-type operators is presented in many texts. This paper…
Set function learning has emerged as a crucial area in machine learning, addressing the challenge of modeling functions that take sets as inputs. Unlike traditional machine learning that involves fixed-size input vectors where the order of…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
Recent times are witnessing rapid development in machine learning algorithm systems, especially in reinforcement learning, natural language processing, computer and robot vision, image processing, speech, and emotional processing and…
These are lecture notes for a simple minicourse approaching the satistical properties of a dynamical system by the study of the associated transfer operator (considered on a suitable functions or measures spaces). The following questions…
In these lecture notes we present an introduction to non-standard analysis especially written for the community of mathematicians, physicists and engineers who do research on J. F. Colombeau' theory of new generalized functions and its…
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…
We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
This paper deals with certain aspects of the vector valued de Branges spaces of entire functions that are based on pairs of Fredholm operator valued functions. Some factorization and isometric embedding results are extended from the scalar…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
The text deals with generalizations of the Markoff equation in number theory, arising from continued fractions. It gives the method for the complete resolution of such new equations, and their interpretation in algebra and algebraic…
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
Non-covalent interactions are essential in the description of soft matter, including materials of technological importance and biological molecules. In density-functional theory, common approaches fail to describe dispersion forces, an…