Harmonic functions | Harmonic analysis | Complex analysis

Positive harmonic function

In mathematics, a positive harmonic function on the unit disc in the complex numbers is characterized as the Poisson integral of a finite positive measure on the circle. This result, the Herglotz-Riesz representation theorem, was proved independently by Gustav Herglotz and Frigyes Riesz in 1911. It can be used to give a related formula and characterization for any holomorphic function on the unit disc with positive real part. Such functions had already been characterized in 1907 by Constantin Carathéodory in terms of the positive definiteness of their Taylor coefficients. (Wikipedia).

Video thumbnail

Linear Functions

Define a linear function. Determine if a linear function is increasing or decreasing. Interpret linear function models. Determine linear functions. Site: http://mathispower4u.com

From playlist Introduction to Functions: Function Basics

Video thumbnail

Compare Linear and Exponential Functions

This video compares linear and exponential functions. http://mathispower4u.com

From playlist Introduction to Exponential Functions

Video thumbnail

Determine if a Function is a Polynomial Function

This video explains how to determine if a function is a polynomial function. http://mathispower4u.com

From playlist Determining the Characteristics of Polynomial Functions

Video thumbnail

Ex 1: Determine Composite Function Values Using Table, Graph, and Function Rule

This video explains how to determine various composite function values using a table, graph, and function rule. Site: http://mathispower4u.com

From playlist Determining Composite Functions and Composite Function Values

Video thumbnail

Ex: Determine if a Linear Function is Increasing or Decreasing

This video explains how to determine if a linear function is increasing or decreasing. The results are discussed graphically. Site: http://mathispower4u.com

From playlist Introduction to Functions: Function Basics

Video thumbnail

Determine Linear Function Values and Express as Ordered Pairs

This video explains how to determine linear function values. Each function value is also expressed as an ordered pair. http://mathispower4u.com

From playlist Determining Function Values

Video thumbnail

Function Arithmetic (Difference): (f-g)(x) and (f-g)(-2) - Quadratic

This video explains how to determine the difference of two quadratic functions. Then a function value is determined using two methods. http://mathispower4u.com

From playlist The Properties of Functions

Video thumbnail

Ex 1: Find the Inverse of a Function

This video provides two examples of how to determine the inverse function of a one-to-one function. A graph is used to verify the inverse function was found correctly. Library: http://mathispower4u.com Search: http://mathispower4u.wordpress.com

From playlist Determining Inverse Functions

Video thumbnail

(New Version Available) Inverse Functions

New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/

From playlist Exponential and Logarithmic Expressions and Equations

Video thumbnail

2022 10 Dan Coman: Extension of quasiplurisubharmonic functions

CONFERENCE Recording during the thematic meeting : "Complex Geometry, Dynamical Sytems and Foliation Theory" the October 20, 2022 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathemat

From playlist Analysis and its Applications

Video thumbnail

Simple Harmonic Motion in Trig (Precalculus - Trigonometry 35)

A brief discussion of Simple Harmonic Motion, how it is related to Sine and Cosine, and the functional models it creates. Support: https://www.patreon.com/ProfessorLeonard

From playlist Precalculus - College Algebra/Trigonometry

Video thumbnail

Simple Harmonic Motion(SHM) - Graphs of Position, Velocity, and Acceleration

Position, velocity, and acceleration as a function of time graphs for an object in simple harmonic motion are shown and demonstrated. Want Lecture Notes? https://www.flippingphysics.com/shm-graphs.html This is an AP Physics 1/JEE/NEET topic. 0:00 Reviewing the equations 1:46 Position grap

From playlist IB Physics 9.1: Simple Harmonic Motion (HL Only)

Video thumbnail

Pengzi Miao - Recent inequalities on the mass-to-capacity ratio

On an asymptotically flat 3-manifold, both the mass and the capacity have unit of length, and hence their ratio is a dimensionless quantity. In this talk, I will discuss recent work on establishing new inequalities for the mass-to-capacity ratio on manifolds with nonnegative scalar curvatu

From playlist Not Only Scalar Curvature Seminar

Video thumbnail

Simple Harmonic Motion Derivations using Calculus (Mass-Spring System)

Calculus is used to derive the simple harmonic motion equations for a mass-spring system. Equations derived are position, velocity, and acceleration as a function of time, angular frequency, and period. Want Lecture Notes? http://www.flippingphysics.com/SHM-derivation-mass-spring.html This

From playlist Simple Harmonic Motion - AP Physics C: Mechanics

Video thumbnail

Daniel Stern - Level set methods for scalar curvature on three-manifolds

We'll discuss a circle of ideas developed over the last few years relating scalar curvature lower bounds to the structure of level sets of solutions to certain geometric pdes on 3-manifolds. We'll describe applications to the study of 3-manifold geometry and initial data sets in general re

From playlist Not Only Scalar Curvature Seminar

Video thumbnail

AP Physics C: Simple Harmonic Motion Review (Mechanics)

Calculus based review of Simple Harmonic Motion (SHM). SHM is defined. A horizontal mass-spring system is analyzed and proven to be in SHM and it’s period is derived. The difference between frequency and angular frequency is shown. The equations and graphs of position, velocity, and accele

From playlist Simple Harmonic Motion - AP Physics C: Mechanics

Video thumbnail

Algebraically Determine If the Rational Function is Even or Odd

👉 Learn how to determine if a function is even or odd. A function is even if the graph of the function is symmetrical about the y-axis, or a function is even if f(x) = f(-x). A function is odd if the graph of the function is symmetrical about the origin, or a function is odd if f(-x) = -f(

From playlist Characteristics of Functions

Video thumbnail

Quantitative propagation for solutions of elliptic equations – A. Logunov & E. Malinnikova – ICM2018

Partial Differential Equations | Geometry Invited Lecture 10.11 | 5.12 Quantitative propagation of smallness for solutions of elliptic equations Alexander Logunov & Eugenia Malinnikova Abstract: Let u be a solution to an elliptic equation div(A∇u)=0 with Lipschitz coefficients in ℝⁿ. Ass

From playlist Geometry

Related pages

Helly's selection theorem | Constantin Carathéodory | Mathematics | Frigyes Riesz | Bochner's theorem | Probability measure | Holomorphic function