Related papers: A guide to Carleson's Theorem
The main goal of this paper is to generalize Bohr's phenomenon from complex one-dimensional analysis to higher dimensions in the framework of Quaternionic Analysis.
This expository essay accompanied the author's presentation at the S\'eminaire Bourbaki on 01 April 2023. It describes the breakthrough work of Du--Zhang on the Carleson problem for the Schr\"odinger equation, together with background…
The purpose of this book is to provide an introduction to period theory and then to place it within the matrix of recursive function theory.
We give an introduction to Tropical Geometry and prove some results in Tropical Intersection Theory. The first part of this paper is an introduction to tropical geometry aimed at researchers in Algebraic Geometry from the point of view of…
A q-type Holder condition on a function f is given in order to establish (uniform) convergence of the corresponding basic Fourier series S_q[f] to the function itself, on the set of points of the q-linear grid. Furthermore, by adding others…
In this paper we consider some results on intersection between rays and a given family of convex, compact sets. These results are similar to the center point theorem, and Tverberg's theorem on partitions of a point set.
This is an intorduction to some of the basic methods and results of dense matter physics.It is aimed at readers interested in astrophysical and physical applications.
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
These notes are a self-contained introduction to Galois theory, designed for the student who has done a first course in abstract algebra.
Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…
We describe a formula for the Taylor series expansion of the Gaussian kernel around the origin of $\Rn\times\R$.
This paper aims to give a coordinate based introduction to the so-called Lounesto spinorial classification scheme. We introduce the main ideas and aspects of this spinorial categorization in an argumentative basis, after what we delve into…
In this paper, we introduce a new type of coupled fixed point theorem in partially ordered complete metric space. We give an example to support of our result.
An introduction to the methods and ideas of Chiral Perturbation Theory is presented in this talk. The discussion is illustrated with some phenomenological predictions that can be compared with available experimental results.
Carlson's theorem estimates the growth of an analytic function along the imaginary axis, provided that the function is zero at non-negative integers. We refine this theorem and describe not only the function's growth but also necessary and…
This primer is intended as an introduction to differential forms, a central object in modern mathematical physics, for scientists and engineers.
The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.
Course material for mathematical methods of theoretical physics intended for an undergraduate audience.
In this article, we prove a quantitative version of Carleson's $\varepsilon^2$ conjecture in higher dimension: we characterise those Ahlfors-David regular domains in $\mathbb{R}^{n+1}$ for which the Carleson's coefficients satisfy the…
This paper serves as an introduction to the current book. It provides the basic notions of long-baseline optical/infrared interferome-try prior to reading all the subsequent chapters, and is not an extended introduction to the field.