Kelvin transform, the Glossary
The Kelvin transform is a device used in classical potential theory to extend the concept of a harmonic function, by allowing the definition of a function which is 'harmonic at infinity'.[1]
Table of Contents
9 relations: Harmonic function, Inversive geometry, John Wermer, Journal de Mathématiques Pures et Appliquées, Lecture Notes in Mathematics, Lord Kelvin, Potential theory, Spherical wave transformation, Subharmonic function.
- Harmonic functions
Harmonic function
In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function f\colon U \to \mathbb R, where is an open subset of that satisfies Laplace's equation, that is, \frac + \frac + \cdots + \frac. Kelvin transform and harmonic function are harmonic functions.
See Kelvin transform and Harmonic function
Inversive geometry
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines and that preserves the angles between crossing curves.
See Kelvin transform and Inversive geometry
John Wermer
John Wermer was a mathematician specializing in Complex analysis.
See Kelvin transform and John Wermer
Journal de Mathématiques Pures et Appliquées
The Journal de Mathématiques Pures et Appliquées is a French monthly scientific journal of mathematics, founded in 1836 by Joseph Liouville (editor: 1836–1874).
See Kelvin transform and Journal de Mathématiques Pures et Appliquées
Lecture Notes in Mathematics
Lecture Notes in Mathematics is a book series in the field of mathematics, including articles related to both research and teaching.
See Kelvin transform and Lecture Notes in Mathematics
Lord Kelvin
William Thomson, 1st Baron Kelvin, (26 June 182417 December 1907) was a British mathematician, mathematical physicist and engineer born in Belfast.
See Kelvin transform and Lord Kelvin
Potential theory
In mathematics and mathematical physics, potential theory is the study of harmonic functions.
See Kelvin transform and Potential theory
Spherical wave transformation
Spherical wave transformations leave the form of spherical waves as well as the laws of optics and electrodynamics invariant in all inertial frames.
See Kelvin transform and Spherical wave transformation
Subharmonic function
In mathematics, subharmonic and superharmonic functions are important classes of functions used extensively in partial differential equations, complex analysis and potential theory.
See Kelvin transform and Subharmonic function
See also
Harmonic functions
- Bôcher's theorem
- Cauchy–Riemann equations
- Differential forms on a Riemann surface
- Dirichlet's principle
- Edmund Schuster
- Harmonic conjugate
- Harmonic coordinates
- Harmonic function
- Harmonic map
- Harmonic morphism
- Harnack's inequality
- Harnack's principle
- Hilbert transform
- Kellogg's theorem
- Kelvin transform
- Laplace operator
- Laplace's equation
- Maximum principle
- Newtonian potential
- Pluriharmonic function
- Poisson kernel
- Positive harmonic function
- Schwarz alternating method
- Schwarz reflection principle
- Weakly harmonic function
- Weyl's lemma (Laplace equation)
References
[1] https://en.wikipedia.org/wiki/Kelvin_transform
Also known as Kelvin inverse, Կելվինի ձևափոխություն.