Difference between revisions of "Index of spaces"
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| + | ==Using the index== | ||
| + | People might use {{M|i}} or {{M|j}} or even {{M|k}} for indicies, as such "numbers" are indexed as "num" (notice the lower-case) so a space like {{M|C^k}} is under {{C|C_num}}. | ||
| + | |||
| + | We do subscripts first, so {{M|A_i^2}} would be under {{M|A_num_2}} | ||
| + | |||
| + | ===Ordering=== | ||
| + | # First come actual numbers. | ||
| + | # Next come {{C|num}} terms. | ||
| + | # Then come {{C|infty}} (which denotes {{M|\infty}} | ||
| + | # Then come letters (upper case) | ||
| + | # Then come brackets {{C|(}} first, then {{C|[}} then {{C|{}} | ||
| + | |||
| + | For example {{M|C_0}} comes before {{M|C_i}} comes before {{M|C_\infty}} comes before {{M|C_\text{text} }} | ||
| + | |||
| + | ==Index== | ||
{| class="wikitable" border="1" | {| class="wikitable" border="1" | ||
|- | |- | ||
| + | ! Space or name | ||
! Index | ! Index | ||
| − | |||
! Context | ! Context | ||
! Meaning | ! Meaning | ||
|- | |- | ||
| − | ! | + | | {{M|C_k\text{ on }U}} |
| + | ! C_num_ON | ||
| + | | | ||
| + | * ''(Everywhere)'' | ||
| + | | '''(SEE ''[[Classes of continuously differentiable functions]]'')''' - a function is {{M|C_k}} on {{M|U}} if {{M|U\subset\mathbb{R}^n}} is open and the partial derivatives of {{M|f:U\rightarrow\mathbb{R}^m}} of all orders (up to and including {{M|k}}) are continuous on {{M|U}} | ||
| + | |- | ||
| + | | {{M|C_k(U)}} | ||
| + | ! C_num_( | ||
| + | | | ||
| + | * ''(Everywhere)'' | ||
| + | | '''(SEE ''[[Classes of continuously differentiable functions]]'')''' - denotes a set, given {{M|U\subseteq\mathbb{R}^n}} (that's open) {{M|f\in C_k(U)}} if {{M|f:U\rightarrow\mathbb{R} }} has continuous partial derivatives of all orders up to and including {{M|k}} on {{M|U}} | ||
| + | |- | ||
| {{M|l_2}} | | {{M|l_2}} | ||
| + | ! L2 | ||
| | | | ||
* Functional Analysis | * Functional Analysis | ||
Revision as of 20:51, 16 October 2015
Using the index
People might use [ilmath]i[/ilmath] or [ilmath]j[/ilmath] or even [ilmath]k[/ilmath] for indicies, as such "numbers" are indexed as "num" (notice the lower-case) so a space like [ilmath]C^k[/ilmath] is under C_num.
We do subscripts first, so [ilmath]A_i^2[/ilmath] would be under [ilmath]A_num_2[/ilmath]
Ordering
- First come actual numbers.
- Next come num terms.
- Then come infty (which denotes [ilmath]\infty[/ilmath]
- Then come letters (upper case)
- Then come brackets ( first, then [ then {
For example [ilmath]C_0[/ilmath] comes before [ilmath]C_i[/ilmath] comes before [ilmath]C_\infty[/ilmath] comes before [ilmath]C_\text{text} [/ilmath]
Index
| Space or name | Index | Context | Meaning |
|---|---|---|---|
| [ilmath]C_k\text{ on }U[/ilmath] | C_num_ON |
|
(SEE Classes of continuously differentiable functions) - a function is [ilmath]C_k[/ilmath] on [ilmath]U[/ilmath] if [ilmath]U\subset\mathbb{R}^n[/ilmath] is open and the partial derivatives of [ilmath]f:U\rightarrow\mathbb{R}^m[/ilmath] of all orders (up to and including [ilmath]k[/ilmath]) are continuous on [ilmath]U[/ilmath] |
| [ilmath]C_k(U)[/ilmath] | C_num_( |
|
(SEE Classes of continuously differentiable functions) - denotes a set, given [ilmath]U\subseteq\mathbb{R}^n[/ilmath] (that's open) [ilmath]f\in C_k(U)[/ilmath] if [ilmath]f:U\rightarrow\mathbb{R} [/ilmath] has continuous partial derivatives of all orders up to and including [ilmath]k[/ilmath] on [ilmath]U[/ilmath] |
| [ilmath]l_2[/ilmath] | L2 |
|
Space of square-summable sequences |
