In mathematical analysis, Lorentz spaces, introduced by George G. Lorentz in the 1950s,[1][2] are generalisations of the more familiar spaces.
The Lorentz spaces are denoted by . Like the spaces, they are characterized by a norm (technically a quasinorm) that encodes information about the "size" of a function, just as the norm does. The two basic qualitative notions of "size" of a function are: how tall is the graph of the function, and how spread out is it. The Lorentz norms provide tighter control over both qualities than the norms, by exponentially rescaling the measure in both the range () and the domain (). The Lorentz norms, like the norms, are invariant under arbitrary rearrangements of the values of a function.
^G. Lorentz, "Some new function spaces", Annals of Mathematics51 (1950), pp. 37-55.
^G. Lorentz, "On the theory of spaces Λ", Pacific Journal of Mathematics1 (1951), pp. 411-429.
Lorentzspaces, introduced by George G. Lorentz in the 1950s, are generalisations of the more familiar L p {\displaystyle L^{p}} spaces. The Lorentz spaces...
electron The Standard Model of particle physics The Lorentz group expresses the fundamental symmetry of space and time of all known fundamental laws of nature...
The Lorentz transformation is a linear transformation. It may include a rotation of space; a rotation-free Lorentz transformation is called a Lorentz boost...
particular, a Lorentz covariant scalar (e.g., the space-time interval) remains the same under Lorentz transformations and is said to be a Lorentz invariant...
Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar...
when events occur within the universe). However, space and time took on new meanings with the Lorentz transformation and special theory of relativity....
In physics, specifically in electromagnetism, the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point...
Hendrik Antoon Lorentz (/ˈlɒrənts/; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman...
own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald contraction (after Hendrik Lorentz and George Francis FitzGerald) and is...
from the work of Hendrik Lorentz, Henri Poincaré, and others said it "was grown on experimental physical grounds". Minkowski space is closely associated...
hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group. In physics, Lorentz transformations...
The Lorentz group is a Lie group of symmetries of the spacetime of special relativity. This group can be realized as a collection of matrices, linear...
What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development...
distances in space or in time separately are not invariant with respect to Lorentz coordinate transformations, but distances in Minkowski space along spacetime...
the Lorentz transformations. Time and space cannot be defined separately from each other (as was previously thought to be the case). Rather, space and...
= p, the Lorentzspace Lp,p is equal to Lp, up to renorming. When q = ∞, the Lorentzspace Lp,∞ is equal to weak-Lp. An intermediate space X of the compatible...
_{f}^{1/p}(t).} The weak L p {\displaystyle L^{p}} coincide with the Lorentzspaces L p , ∞ , {\displaystyle L^{p,\infty },} so this notation is also used...
results and empirical findings obtained by Albert A. Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did...
the electromagnetic field is described by Maxwell's equations and the Lorentz force law. Maxwell's equations detail how the electric field converges...
of Lorentz and Poincaré, could best be understood in a four-dimensional space, since known as the "Minkowski spacetime", in which time and space are...
standard dot product is used in Minkowski space: R 4 {\displaystyle \mathbf {R} ^{4}} endowed with the Lorentz product ⟨ x | y ⟩ = x 1 y 1 + x 2 y 2 + x...
Global Information
