Real analysis | Harmonic analysis | Tauberian theorems
In mathematical analysis, Wiener's tauberian theorem is any of several related results proved by Norbert Wiener in 1932. They provide a necessary and sufficient condition under which any function in L1 or L2 can be approximated by linear combinations of translations of a given function. Informally, if the Fourier transform of a function f vanishes on a certain set Z, the Fourier transform of any linear combination of translations of f also vanishes on Z. Therefore, the linear combinations of translations of f can not approximate a function whose Fourier transform does not vanish on Z. Wiener's theorems make this precise, stating that linear combinations of translations of f are dense if and only if the zero set of the Fourier transform of f is empty (in the case of L1) or of Lebesgue measure zero (in the case of L2). Gelfand reformulated Wiener's theorem in terms of commutative C*-algebras, when it states that the spectrum of the L1 group ring L1(R) of the group R of real numbers is the dual group of R. A similar result is true when R is replaced by any locally compact abelian group. (Wikipedia).
Applying reimann sum for the midpoint rule and 3 partitions
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Bertrand Eynard: Integrable systems and spectral curves
Usually one defines a Tau function Tau(t_1,t_2,...) as a function of a family of times having to obey some equations, like Miwa-Jimbo equations, or Hirota equations. Here we shall view times as local coordinates in the moduli-space of spectral curves, and define the Tau-function of a spect
From playlist Analysis and its Applications
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Yuri Tschinkel, Height zeta functions
VaNTAGe seminar May 11, 2021 License: CC-BY-NC-SA
From playlist Manin conjectures and rational points
Weil conjectures 1 Introduction
This talk is the first of a series of talks on the Weil conejctures. We recall properties of the Riemann zeta function, and describe how Artin used these to motivate the definition of the zeta function of a curve over a finite field. We then describe Weil's generalization of this to varie
From playlist Algebraic geometry: extra topics
Midpoint riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Large deviations for the Wiener Sausage by Frank den Hollander
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
Infinite products & the Weierstrass factorization theorem
In this video we're going to explain the Weierstrass factorization theorem, giving rise to infinite product representations of functions. Classical examples are that of the Gamma function or the sine function. https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem https://en.wiki
From playlist Programming
Emanuele Di Benedetto - Tribute to Ennio De Giorgi - 20 September 2016
Di Benedetto , Emmanuele "A Wiener-type condition for bound- ary continuity of quasi-minima of variational integrals"
From playlist A Mathematical Tribute to Ennio De Giorgi
Jacob Lurie: 1/5 Tamagawa numbers in the function field case [2019]
Slides for this talk: http://swc-alpha.math.arizona.edu/video/2019/2019LurieLecture1Slides.pdf Lecture notes: http://swc.math.arizona.edu/aws/2019/2019LurieNotes.pdf Let G be a semisimple algebraic group defined over the field Q of rational numbers and let G(Q) denote the group of ration
From playlist Number Theory
Large deviations for the Wiener Sausage (Lecture 2) by Frank den Hollander
Large deviation theory in statistical physics: Recent advances and future challenges DATE: 14 August 2017 to 13 October 2017 VENUE: Madhava Lecture Hall, ICTS, Bengaluru Large deviation theory made its way into statistical physics as a mathematical framework for studying equilibrium syst
From playlist Large deviation theory in statistical physics: Recent advances and future challenges
La théorie l’information sans peine - Bourbaphy - 17/11/18
Olivier Rioul (Telecom Paris Tech) / 17.11.2018 La théorie l’information sans peine ---------------------------------- Vous pouvez nous rejoindre sur les réseaux sociaux pour suivre nos actualités. Facebook : https://www.facebook.com/InstitutHenriPoincare/ Twitter : https://twitter.com
From playlist Bourbaphy - 17/11/18 - L'information
How to use right hand riemann sum give a table
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Introduction to number theory lecture 47. The prime number theorem
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We give an overview of the prime number theorem, stating that the number of primes less tha
From playlist Introduction to number theory (Berkeley Math 115)
Corinne Blondel - Godement le professeur, Godement l'objecteur
Godement le mathématicien était un enseignant hors pair, transmettant sa passion pour les mathématiques dans toute son exigence sans jamais omettre de rappeler la responsabilité morale du scientifique. Son Cours d'Algèbre est emblématique de cette démarche, ainsi que les volumes d'Analyse
From playlist Reductive groups and automorphic forms. Dedicated to the French school of automorphic forms and in memory of Roger Godement.
Yair Shenfeld - The Brownian transport map - IPAM at UCLA
Recorded 09 February 2022. Yair Shenfeld of the Massachusetts Institute of Technology presents "The Brownian transport map" at IPAM's Calculus of Variations in Probability and Geometry Workshop. Abstract: The existence of Lipschitz transport maps between probability measures leads to tran
From playlist Workshop: Calculus of Variations in Probability and Geometry
Right hand riemann sum approximation
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Gamma derive: https://youtu.be/0170T
From playlist Limits
High-Energy Conformal Bootstrap and Tauberian Theory - Baurzhan Mukhametzhanov
More videos on http://video.ias.edu
From playlist Natural Sciences