In this video, I prove the famous Riemann-Lebesgue lemma, which states that the Fourier transform of an integrable function must go to 0 as |z| goes to infinity. This is one of the results where the proof is more important than the theorem, because it's a very classical Lebesgue integral
From playlist Real Analysis
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
Background material on the Cauchy-Riemann equations (Lecture 1) by Debraj Chakrabarti
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
This talk is the first of two talks that give a proof of the Riemann Roch theorem, in the spacial case of nonsingular complex plane curves. We divide the Riemann-Roch theorem into 3 pieces: Riemann's theorem, a topological theorem identifying the three definitions of the genus, and Roch'
From playlist Algebraic geometry: extra topics
Lefschetz Fixed Point Theorem example
Here we give an example of how to use the Lefschetz fixed point theorem. These notes were really useful as a graduate student, some of them are down now, but I think these notes I had came from here: http://mathsci.kaist.ac.kr/~jinhyun/useful.html
From playlist Riemann Hypothesis
This talk is about some properties of plane curves used in the Riemann-Roch theorem. We first show that every nonsingular curve is isomorphic to a resolution of a plane curve with no singularities worse than ordinary double points (nodes). We then calculate the genus of plane curves with o
From playlist Algebraic geometry: extra topics
Ch 6: What are bras and bra-ket notation? | Maths of Quantum Mechanics
Hello! This is the sixth chapter in my series "Maths of Quantum Mechanics." In this episode, we'll intuitively understand what the bra is in quantum mechanics, and why we need it. We'll also finally justify the power of bra-ket notation, and its relation to the Riesz representation theore
From playlist Maths of Quantum Mechanics
Markus Haase : Operators in ergodic theory - Lecture 1 : Operators dynamics versus ...
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 6
From playlist Jean-Morlet Chair - Lemanczyk/Ferenczi
Functional Analysis Lecture 06 2014 02 06 Riesz Interpolation Theorem, Part 1
Fourier coefficients; Fourier series; connection with complex analysis (conjugate function; Cauchy integral); Riesz interpolation; Hausdorff-Young inequality; “three lines” lemma. Note there is an error in the statement of the interpolation theorem: p_i and q_i need not be conjugate expon
From playlist Course 9: Basic Functional and Harmonic Analysis
Riemann Sum Defined w/ 2 Limit of Sums Examples Calculus 1
I show how the Definition of Area of a Plane is a special case of the Riemann Sum. When finding the area of a plane bound by a function and an axis on a closed interval, the width of the partitions (probably rectangles) does not have to be equal. I work through two examples that are rela
From playlist Calculus
What is the Riemann Hypothesis?
This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation
From playlist Mathematics
Functional Analysis - Part 15 - Riesz Representation Theorem
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Functional analysis series: https://www.youtube.com/playlist?list=PLBh2i93oe2qsGKDOsuVVw-OCAfprrnGfr PDF versions: https://steadyhq.com/en/brightsideofmaths/po
From playlist Functional analysis
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
Math 131 Spring 2022 050422 Riemann-Lebesgue lemma; Classical Fourier Series.
Recall definition of orthonormal systems. Results about General Fourier Series: Proof of "Best Mean Square Approximation" (that the partial sum of the Fourier series of a (Riemann integrable) function is the best linear combination approximating the function in the L2 sense). Consequence
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
MAST30026 Lecture 20: Hilbert space (Part 2)
I continued with the basic theory of inner product spaces and Hilbert spaces, by defining orthogonal complements and proving that every closed vector subspace of a Hilbert space gives rise to a direct sum decomposition of the Hilbert space. Then we proved the Riesz representation theorem,
From playlist MAST30026 Metric and Hilbert spaces
The Field With One Element and The Riemann Hypothesis (Full Video)
A crash course of Deninger's program to prove the Riemann Hypothesis using a cohomological interpretation of the Riemann Zeta Function. You can Deninger talk about this in more detail here: http://swc.math.arizona.edu/dls/ Leave some comments!
From playlist Riemann Hypothesis
Measure Theory 3.3 : Riemann Integral Equals Lebesgue Integral
In this video, I describe a new way of defining the Riemann Integral, and use that to prove that the Riemann and Lebesgue Integrals are the same for Riemann Integrable functions. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet
From playlist Measure Theory
Math 131 Spring 2022 050422 Riesz Fischer; Parseval's theorem
Riesz-Fischer theorem: Fourier Series of a (Riemann integrable) function converge to the original function - in the L2 sense. Consequence: Parseval's theorem: the L2 norm of the function is the l2 norm of its Fourier coefficients.
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Kai Zeng - Schatten Properties of Commutators
Given a quantum tori $\mathbb{T}_{\theta}^d$, we can define the Riesz transforms $\mathfrak{R}_j$ on the quantum tori and the commutator $đx_i$ := [$\mathfrak{R}_i,M_x$], where $M_x$ is the operator on $L^2(\mathbb{T}_{\theta}^d)$ of pointwise multiplication by $x \in L^\infty (\mathbb{T}_
From playlist Annual meeting “Arbre de Noël du GDR Géométrie non-commutative”
These are some definitions about infinite products. You shouldn't watch this video.
From playlist Riemann Hypothesis