Math 139 Fourier Analysis Lecture 32: Fourier Analysis on Finite Abelian Groups
Proving that the dual group has the same order as the group (to show the characters form an orthonormal basis for the functions on the group). Fourier analysis on finite abelian groups: Fourier coefficients; Fourier series; Fourier inversion formula; Plancherel/Parseval theorem. Statemen
From playlist Course 8: Fourier Analysis
The Fourier Transform and Derivatives
This video describes how the Fourier Transform can be used to accurately and efficiently compute derivatives, with implications for the numerical solution of differential equations. Book Website: http://databookuw.com Book PDF: http://databookuw.com/databook.pdf These lectures follow
From playlist Fourier
Introduction to additive combinatorics lecture 7.3 -- dual groups and the discrete Fourier transform
The discrete Fourier transform is a fundamental tool in additive combinatorics that makes it possible to prove many interesting results that would be very hard or even impossible to prove otherwise. Here I discuss the characters on a finite Abelian group G, prove that they are orthogonal a
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Math 139 Fourier Analysis Lecture 30: FFT ct'd; Fourier Analysis on Finite Abelian Groups
Proof of key lemma for Fast Fourier Transform. Fourier Analysis on Finite Abelian Groups: abelian groups; unit; order of a group; group homomorphism; isomorphism; direct product of abelian groups; structure theorem for finite abelian groups; characters; dual group
From playlist Course 8: Fourier Analysis
What is a Fourier Transform and how does it relate to the Fourier Series? In this video, we discuss the idea of the Fourier Cosine Transform.
From playlist Mathematical Physics II Uploads
Fourier Series (for PDEs) w/ Fourier Polynomials (Orthogonal Projections in Inner Product Spaces)
Fourier Series (for Partial Differential Equations) are Constructed with Fourier Polynomials, which are Orthogonal Projections in Inner Product Spaces (in this case, the Function Space of Real-Valued Continuous Functions C[-pi,pi] with the inner product of f and g defined to be the integra
From playlist Fourier
What is the Fourier Transform?
In this video, we'll look at the fourier transform from a slightly different perspective than normal, and see how it can be used to estimate functions. Learn about the Fourier series here: http://youtu.be/kP02nBNtjrU
From playlist Fourier
Electrical Engineering: Ch 19: Fourier Transform (2 of 45) What is a Fourier Transform? Math Def
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the mathematical definition and equation of a Fourier transform. Next video in this series can be seen at: https://youtu.be/yl6RtWp7y4k
From playlist ELECTRICAL ENGINEERING 18: THE FOURIER TRANSFORM
18. Roth's theorem I: Fourier analytic proof over finite field
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX The finite field model is a nice sandbox for methods and
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
CTNT 2022 - p-adic Fourier theory and applications (by Jeremy Teitelbaum)
This video is one of the special guess talks or conference talks that took place during CTNT 2022, the Connecticut Summer School and Conference in Number Theory. Note: not every special guest lecture or conference lecture was recorded. More about CTNT: https://ctnt-summer.math.uconn.edu/
From playlist CTNT 2022 - Conference lectures and special guest lectures
Introduction to additive combinatorics lecture 7.9 --- Basic Fourier transform properties
Here I say a bit more about the discrete Fourier transform, including giving direct proofs of the basic properties that are used over and over again in arguments. As an example of how it relates to additive combinatorics, I show that the additive energy of a set can be expressed in a very
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
Maryna Viazovska (EPFL): Fourier interpolation
This lecture is about Fourier uniqueness and Fourier interpolation pairs. Suppose that we have two subsets X and Y of the Euclidean space. Can we reconstruct a function f from its restriction to the set X and the restriction of its Fourier transform to the set Y? We are interested in the p
From playlist Seminar Series "Arithmetic Applications of Fourier Analysis"
RT7.2. Finite Abelian Groups: Fourier Analysis
Representation Theory: With orthogonality of characters, we have an orthonormal basis of L^2(G). We note the basic philosophy behind the Fourier transform and apply it to the character basis. From this comes the definition of convolution, explored in 7.3. Course materials, including pro
From playlist Representation Theory
Fourier transform for Class D-modules - David Ben Zvi
Locally Symmetric Spaces Seminar Topic: Fourier transform for Class D-modules Speaker: David Ben Zvi Affiliation: University of Texas at Austin; Member, School of Mathematics Date: Febuary 13, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Math 131 Fall 2018 121218 Advertising the Fourier Analysis course
Advertising Math 139: Fourier Analysis. Ubiquitous. Applications. Fourier Series: application (isoperimetric inequality). Fourier transform; application (Radon transform). Fourier series on finite abelian groups; application (Dirichlet's theorem). Brief introduction to Fourier series
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
The Discrete Fourier Transform
This video provides a basic introduction to the very widely used and important discrete Fourier transform (DFT). The DFT describes discrete-time signals as a weighted sum of complex sinusoid building blocks and is used in applications such as GPS, MP3, JPEG, and WiFi.
From playlist Fourier
Theta intertwining sheaves - Zhiwei Yun
Virtual Workshop on Recent Developments in Geometric Representation Theory Topics: Theta intertwining sheaves Speaker: Zhiwei Yun Affiliation: Massachusetts Institute of Technology Date: November 16, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
On triple product L functions - Jayce Robert Getz
Joint IAS/Princeton University Number Theory Seminar Topic: On triple product L functions Speaker: Jayce Robert Getz Affiliation: Duke University Date: May 7, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Intro to Fourier series and how to calculate them
Download the free PDF from http://tinyurl.com/EngMathYT This is a basic introduction to Fourier series and how to calculate them. An example is presented that illustrates the computations involved. Such ideas are seen in university mathematics.
From playlist Fourier