Weak convergence (Hilbert space)

Convergence in Rn

Convergence in Rn. In this video, I define what it means for a sequence to converge in R^n (and more generally in metric spaces) and prove the important fact that a sequence in R^n converges if and only if each of its component converges. Enjoy this beautiful real analysis and math extrava

From playlist Topology

Math 131 Spring 2022 030922 Sequences in metric spaces

Sequences in metric spaces: convergence, divergence, remark that convergence is dependent on the metric and the space. Properties of convergence: neighborhood characterization, uniqueness of limit, boundedness of convergent sequence, existence of a convergent sequence to a limit point of a

From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)

Math 139 Fourier Analysis Lecture 09: L^2 convergence of the Fourier Series

L^2 convergence of Fourier Series: little l^2; l^2 is a vector space; the space of integrable functions on the circle; Fourier series of an integrable function converges to the function in the sense of L^2

From playlist Course 8: Fourier Analysis

What is Length Contraction?

What is length contraction? Length contraction gives the second piece (along with time dilation) of the puzzle that allows us to reconcile the fact that the speed of light is constant in all reference frames.

From playlist Relativity

Calculus: How Convergence Explains The Limit

The limit definition uses the idea of convergence twice (in two slightly different ways). Once the of convergence is grasped, the limit concept becomes easy, even trivial. This clip explains convergence and shows how it can be used to under the limit.

From playlist Summer of Math Exposition Youtube Videos

MAST30026 Lecture 20: Hilbert space (Part 3)

I prove that L^2 spaces are Hilbert spaces. Lecture notes: http://therisingsea.org/notes/mast30026/lecture20.pdf The class webpage: http://therisingsea.org/post/mast30026/ Have questions? I hold free public online office hours for this class, every week, all year. Drop in and say Hi! For

From playlist MAST30026 Metric and Hilbert spaces

Complete Statistical Theory of Learning (Vladimir Vapnik) | MIT Deep Learning Series

Lecture by Vladimir Vapnik in January 2020, part of the MIT Deep Learning Lecture Series. Slides: http://bit.ly/2ORVofC Associated podcast conversation: https://www.youtube.com/watch?v=bQa7hpUpMzM Series website: https://deeplearning.mit.edu Playlist: http://bit.ly/deep-learning-playlist

From playlist AI talks

Hans Feichtinger: Fourier Analysis via the Banach Gelfand Triple

The lecture was held within the framework of the Hausdorff Trimester Program Mathematics of Signal Processing. In this MATLAB-based presentation the author will explain how one can understand and illustrate the foundations of Gabor analysis with the help of MATLAB. From the point of view

From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"

Find the Interval of Convergence

How to find the interval of convergence for a power series using the root test.

From playlist Convergence (Calculus)

Hans G. Feichtinger: Mathematical and numerical aspects of frame theory - Part 2

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

Lec 22 | MIT 18.085 Computational Science and Engineering I

Fourier expansions and convolution A more recent version of this course is available at: http://ocw.mit.edu/18-085f08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.085 Computational Science & Engineering I, Fall 2007

Markus Haase : Operators in ergodic theory - Lecture 3 : Compact semigroups and splitting theorems

Abstract : The titles of the of the individual lectures are: 1. Operators dynamics versus base space dynamics 2. Dilations and joinings 3. Compact semigroups and splitting theorems Recording during the thematic meeting : "Probabilistic Aspects of Multiple Ergodic Averages " the December 8

From playlist Dynamical Systems and Ordinary Differential Equations

Math 131 Fall 2018 111618 Uniform convergence, continued

Review of uniform convergence: definition and Cauchy criterion. Rephrasal of uniform convergence. Weierstrass M-test for uniform convergence of a series. Uniform convergence and continuous functions. Pointwise convergence of a decreasing sequence of continuous functions on a compact se

From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)

Benjamin Stamm - Eigenvalue problems and error control - IPAM at UCLA

Recorded 10 March 2022. Benjamin Stamm of RWTH Aachen University presents "Eigenvalue problems and error control" at IPAM's Advancing Quantum Mechanics with Mathematics and Statistics Tutorials. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/advancing-quantum-mechanics-w

From playlist Tutorials: Advancing Quantum Mechanics with Mathematics and Statistics - March 8-11, 2022

Erez Lapid - 1/2 Some Perspectives on Eisenstein Series

This is a review of some developments in the theory of Eisenstein series since Corvallis. Erez Lapid (Weizmann Institute)

From playlist 2022 Summer School on the Langlands program

Alexander Bufetov: Determinantal point processes - Lecture 2

Abstract: Determinantal point processes arise in a wide range of problems in asymptotic combinatorics, representation theory and mathematical physics, especially the theory of random matrices. While our understanding of determinantal point processes has greatly advanced in the last 20 year

From playlist Probability and Statistics

Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 5) by Dror Varolin

PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo

From playlist Cauchy-Riemann Equations in Higher Dimensions 2019

From metric spaces to topological spaces -- Proofs

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

Amit Einav: Weak Poincaré inequalities in the absence of spectral gaps

The lecture was held within the framework of the Hausdorff Trimester Program: Kinetic Theory Abstract: Weak Poincaré inequalities in the absence of spectral gaps Abstract: Poincaré inequality, which is probably best known for its applications in PDEs and calculus of variation, is one of

From playlist Workshop: Probabilistic and variational methods in kinetic theory

Functional Analysis Lecture 12 2014 03 04 Boundedness of Hilbert Transform on Hardy Space (part 1)

Dyadic Whitney decomposition needed to extend characterization of Hardy space functions to higher dimensions. p-atoms: definition, have bounded Hardy space norm; p-atoms can also be used in place of atoms to define Hardy space. The Hilbert Transform is bounded from Hardy space to L^1: b

From playlist Course 9: Basic Functional and Harmonic Analysis