Integral transforms | Harmonic analysis | Singular integrals | Potential theory
In the mathematical theory of harmonic analysis, the Riesz transforms are a family of generalizations of the Hilbert transform to Euclidean spaces of dimension d > 1. They are a type of singular integral operator, meaning that they are given by a convolution of one function with another function having a singularity at the origin. Specifically, the Riesz transforms of a complex-valued function ƒ on Rd are defined by for j = 1,2,...,d. The constant cd is a dimensional normalization given by where ωd−1 is the volume of the unit (d − 1)-ball. The limit is written in various ways, often as a principal value, or as a convolution with the tempered distribution The Riesz transforms arises in the study of differentiability properties of harmonic potentials in potential theory and harmonic analysis. In particular, they arise in the proof of the Calderón-Zygmund inequality . (Wikipedia).
Integration 1 Riemann Sums Part 1 - YouTube sharing.mov
Introduction to Riemann Sums
From playlist Integration
Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erkläre ich kurz das Riemann-Integral mit Ober- und Untersumme. Die Definition ist übliche, die im 1. Semester eingeführt w
From playlist 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
What is an enlargement dilation
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
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
👉 Learn about dilations. Dilation is the transformation of a shape by a scale factor to produce an image that is similar to the original shape but is different in size from the original shape. A dilation that creates a larger image is called an enlargement or a stretch while a dilation tha
From playlist Transformations
Michael Baake: A cocycle approach to the Fourier transform of Rauzy fractals...
"A cocycle approach to the Fourier transform of Rauzy fractals and the point spectrumof Pisot inflation tilings" The lecture was held within the framework of the Hausdorff Trimester Program "Dynamics: Topology and Numbers": Conference on “Transfer operators in number theory and quantum ch
From playlist Conference: Transfer operators in number theory and quantum chaos
Multivariable Calculus | Transformations of the plane.
Working towards a formula for change of variables in multiple integrals, we introduce the notion of a one to one transformation of the plane. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus | Multiple Integrals
Animated Mandelbrot Transform - linear interpolation, applied to an image of the Set itself
http://code.google.com/p/mandelstir/
From playlist mandelstir
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 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
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)
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
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”
Gravitational radiation from post-Newtonian sources.... by Luc Blanchet (Lecture - 3)
PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.
From playlist Summer School on Gravitational Wave Astronomy -2019
Animated Mandelbrot transform - linear interpolation
http://code.google.com/p/mandelstir/
From playlist mandelstir