Related papers: Potpourri
These notes briefly consider convolutions of tempered distributions with functions in the Schwartz class.
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
The purpose of this short note is to show the interplay between math outreach and conducting original research, in particular how each can build off the other.
Fourier Series is the second of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such as partial…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
The notes contain a streamlined account on stability of univariate polynomials and related problems
These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.
These lecture notes provide an introduction to quantum information and quantum computation, which are strongly related disciplines and subject of intense research. The lecture notes contain only a small selection of topics in these…
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
These notes deal with a few aspects of Lie algebras and Lie groups, including some matters related to exponentiation.
This is a series of lecture notes explaining topos theory and its application in physics.
The paper is a survey of notions and results related to classical and new generalizations of the notion of a periodic sequence. The topics related to almost periodicity in combinatorics on words, symbolic dynamics, expressibility in logical…
We provide an introduction to mathematical theory of scattering resonances and survey some recent results.
This is a very basic introduction to some notions related to logic and complexity.
We approach several themes of classical geometry of the circle and complete them with some original results, showing that not everything in traditional math is revealed, and that it still has an open character. The topics were chosen…
These are notes from a basic course in Several Complex Variables
In this note, we offer a palatable introduction to the field of arithmetic dynamics. That is, we study the patterns that arise when iterating a polynomial map. This note is accessible to those who have taken an introductory proof based…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Can we use mathematics, and in particular the abstract branch of category theory, to describe some basics of dance, and to highlight structural similarities between music and dance? We first summarize recent studies between mathematics and…