Related papers: A guide to Carleson's Theorem

Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…

We consider row sequences of simultaneous rational approximations constructed in terms of Fourier expansions and prove a Montessus de Ballore type theorem.

The aim of this survey papier is to present a result due to Eisenstein, to prove a generalized version of it, and to present some applications of this Eisenstein's Theorem, in particular to the study of the algebraic closure of the field of…

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.

The main result is a generalization of Keller's recursion equation for finding a prime number given the previous primes. We also examine the convergence of the limit in Keller's equation and the convergence of the limit in the general…

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

The main objective of this paper is to study the existence of solutions to some basic fractional difference equations. The tools employed are Krasnosel'skii fixed point theorem which guarantee at least two positive solutions.

This papper aims to present and demonstrate Clifford's version for a generalization of Miquel's theorem with the use of Euclidean geometry arguments only.

We present a new result on uniform attractivity of the origin for nonlinear time-varying systems. Our theorem generalizes Matrosov's theorem which extends, in a certain manner, Krasovskii-LaSalle invariance principle to the case of general…

In this paper, we present the general one-dimensional Clifford Fourier Transform. We derive fundamental properties: Plancherel theorem, reconstruction and convolution formulas. Additionally, we provide an application to probability theory…

This paper collects many results on galoisian ideals and Galois theory.

Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…

This is an expository introduction to simplicial sets and simplicial homotopy theory with particular focus on relating the combinatorial aspects of the theory to their geometric/topological origins. It is intended to be accessible to…

Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their…

The aim of this article is to study rational parallelisms of algebraic varieties by means of the transcendence of their symmetries. The nature of this transcendence is measured by a Galois group built from the Picard-Vessiot theory of…

We translate Penrose's singularity theorem to a Finsler spacetime. To that end, causal concepts in Lorentzian geometry are extended, including definitions and properties of focal points and trapped surfaces, with careful attention paid to…

This note compares two quantitative versions of the Nonlinear Carleson Conjecture (NCC). We provide motivations for our conjectures and show that they both imply the NCC. We discuss the connection to Carleson-Hunt maximal functions and give…

These notes are an exposition of Galois Theory from the original Lagrangian and Galoisian point of view. A particular effort was made here to better understand the connection between Lagrange's purely combinatorial approach and Galois…

The aim of this paper is to give an introduction to our axiomatic logical analysis of relativity theories.

The convergence theory for the set of simultaneously $\psi$-approximable points lying on a planar curve is established. Our results complement the divergence theory developed in `Diophantine approximation on planar curves and the…