Difference between revisions of "Index of notation"

From Maths
Jump to: navigation, search
m
m
Line 26: Line 26:
 
| <math>\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}</math> - it is a [[Norm]] on <math>\mathcal{C}([0,1],\mathbb{R})</math>
 
| <math>\|f\|_{L^p}=\left(\int^1_0|f(t)|^pdt\right)^\frac{1}{p}</math> - it is a [[Norm]] on <math>\mathcal{C}([0,1],\mathbb{R})</math>
 
|-
 
|-
| <math>C([a,b],\mathbb{R})</math>
+
| <math>\|f\|_\infty</math>
|  
+
|
 
* Functional Analysis
 
* Functional Analysis
 
* Real Analysis
 
* Real Analysis
| It is the set of all functions <math>:[a,b]\rightarrow\mathbb{R}</math> that are [[Continuous map|continuous]]
+
| It is a norm on <math>C([a,b],\mathbb{R})</math>, given by <math>\|f\|_\infty=\sup_{x\in[a,b]}(|f(x)|)</math>
 
|-
 
|-
 
| <math>C^k([a,b],\mathbb{R})</math>
 
| <math>C^k([a,b],\mathbb{R})</math>

Revision as of 13:33, 18 March 2015

Ordered symbols are notations which are (likely) to appear as they are given here, for example C([a,b],R) denotes the continuous function on the interval [a,b] that map to R - this is unlikely to be given any other way because "C" is for continuous.

Ordered symbols

These are ordered by symbols, and then by LaTeX names secondly, for example A comes before A comes before A

Expression Context Details
  • Functional Analysis
  • Real Analysis
Denotes the Norm of a vector
fCk
  • Functional Analysis
This Norm is defined by fCk=ki=0supt[0,1](|f(i)(t)|) - note f(i) is the ith derivative.
fLp
  • Functional Analysis
fLp=(10|f(t)|pdt)1p - it is a Norm on C([0,1],R)
f
  • Functional Analysis
  • Real Analysis
It is a norm on C([a,b],R), given by f=supx[a,b](|f(x)|)
Ck([a,b],R)
  • Functional Analysis
  • Real Analysis
It is the set of all functions :[a,b]R that are continuous and have continuous derivatives up to (and including) order k

The unit interval will be assumed when missing

iAi Makes it explicit that the items in the union (the Ai) are pairwise disjoint, that is for any two their intersection is empty
p(F)
  • Functional Analysis
The set of all bounded sequences, that is p(F)={(x1,x2,...)|xiF, i=1|xi|p<}
Lp
  • Measure Theory
Lp(μ)={u:XR|uM, |u|pdμ<}, p[1,)R

(X,A,μ) is a measure space. The class of all measurable functions for which |f|p is integrable

Lp
  • Measure Theory
Same as Lp

Unordered symbols

Expression Context Details
A/B-measurable
  • Measure Theory
There exists a Measurable map between the σ-algebras