Math 139 Fourier Analysis Lecture 16: Basic Properties of the Fourier Transform
Fourier transform on Schwartz class functions. Interaction of Fourier transform with translations, etc.; closure of Schwartz class under Fourier transform. The Gaussian: definition; Gaussian is preserved by Fourier transform.
From playlist Course 8: Fourier Analysis
Determine the Kernel of a Linear Transformation Given a Matrix (R3, x to 0)
This video explains how to determine the kernel of a linear transformation.
From playlist Kernel and Image of Linear Transformation
Determine a Basis for the Kernel of a Matrix Transformation (3 by 4)
This video explains how to determine a basis for the kernel of a matrix transformation.
From playlist Kernel and Image of Linear Transformation
Functional Analysis Lecture 07 2014 02 11 Riesz Interpolation Theorem, Part 2
Proof of theorem in case of general L^p functions. Using Riesz interpolation to extend Fourier transform. Rapidly decreasing functions; Schwartz class functions. Fourier transform of a Schwartz class function. Properties of Fourier transform (interaction with basic operations); Fourie
From playlist Course 9: Basic Functional and Harmonic Analysis
Proof that the Kernel of a Linear Transformation is a Subspace
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Kernel of a Linear Transformation is a Subspace
From playlist Proofs
Some identities involving the Riemann-Zeta function.
After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist The Riemann Zeta Function
Lecture 24 | The Fourier Transforms and its Applications
Lecture by Professor Brad Osgood for the Electrical Engineering course, The Fourier Transforms and its Applications (EE 261). Professor Osgood continues his lecture on linear systems. The Fourier transform is a tool for solving physical problems. In this course the emphasis is on rela
From playlist Lecture Collection | The Fourier Transforms and Its Applications
Universal optimality proof by Abhinav Kumar
DISCUSSION MEETING SPHERE PACKING ORGANIZERS: Mahesh Kakde and E.K. Narayanan DATE: 31 October 2019 to 06 November 2019 VENUE: Madhava Lecture Hall, ICTS Bangalore Sphere packing is a centuries-old problem in geometry, with many connections to other branches of mathematics (number the
From playlist Sphere Packing - 2019
Understanding and computing the Riemann zeta function
In this video I explain Riemann's zeta function and the Riemann hypothesis. I also implement and algorithm to compute the return values - here's the Python script:https://gist.github.com/Nikolaj-K/996dba1ff1045d767b10d4d07b1b032f
From playlist Programming
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"
Notwithstanding the fact that I introduce the topic as the orbit stabilizer syndrome, this video takes you through the orbit stabilizer theorem. :-) It states that the number of cosets formed by the stabilizer of a group (called the index) is the same as the number of elements in the orbi
From playlist Abstract algebra
Lecture 16: Fejer’s Theorem and Convergence of Fourier Series
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=8IxHMVf3jcA&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Math 139 Fourier Analysis Lecture 23: Heisenberg Uncertainty, Fourier Transform on R^d background
Heisenberg uncertainty principle: state function, expectation, variance; statement of principle; proof. Fourier transform on R^d background: multi-index notation; rotations; rapidly decreasing function; functions of moderate decrease; polar integrals. Elementary theory of the Fourier Tr
From playlist Course 8: Fourier Analysis
Erik van Erp: Lie groupoids in index theory 2
The lecture was held within the framework of the Hausdorff Trimester Program Non-commutative Geometry and its Applications. 9.9.2014
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Lecture 18: The Adjoint of a Bounded Linear Operator on a Hilbert Space
MIT 18.102 Introduction to Functional Analysis, Spring 2021 Instructor: Dr. Casey Rodriguez View the complete course: https://ocw.mit.edu/courses/18-102-introduction-to-functional-analysis-spring-2021/ YouTube Playlist: https://www.youtube.com/watch?v=BctaYoR9tOY&list=PLUl4u3cNGP63micsJp_
From playlist MIT 18.102 Introduction to Functional Analysis, Spring 2021
Erik van Erp: Pseudodifferential Calculi and Groupoids
In recent work Debord and Skandalis realized pseudodifferential operators (on an arbitrary Lie groupoid G) as integrals of certain smooth kernels on the adiabatic groupoid of G. We propose an alternative definition of pseudodifferential calculi (including nonstandard calculi like the Heise
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
Kyle Broder -- Recent Developments Concerning the Schwarz Lemma
A lecture I gave at the Beijing International Center for Mathematical Research geometric analysis seminar. The title being Recent Developments Concerning the Schwarz Lemma with applications to the Wu--Yau Theorem. This contains some recent results concerning the Bochner technique for the G
From playlist Research Lectures
Maryna Viazovska - 2/6 Automorphic Forms and Optimization in Euclidean Space
Hadamard Lectures 2019 The goal of this lecture course, “Automorphic Forms and Optimization in Euclidean Space”, is to prove the universal optimality of the E8 and Leech lattices. This theorem is the main result of a recent preprint “Universal Optimality of the E8 and Leech Lattices and I
From playlist Hadamard Lectures 2019 - Maryna Viazovska - Automorphic Forms and Optimization in Euclidean Space
Functional Analysis Lecture 16 2014 03 25 Tempered Distributions
Recall definition of tempered distributions. Elementary properties. Continuity of tempered distribution with respect to a single Schwartz class norm; extension of compactly supported distributions to tempered distributions. Construction of tempered distributions from functions. Derivat
From playlist Course 9: Basic Functional and Harmonic Analysis