What Is the \|f\|_{C^{1}} Norm?

  • Thread starter Thread starter Smitty_687
  • Start date Start date
  • Tags Tags
    Norm
Smitty_687
Messages
2
Reaction score
0
So, I'm working my way through a proof, which has been fine so far, except I've hit a bit of notation which has stumped me.

Essentially, I have a diffeomorphism f: \mathbb{R}^{n} \to \mathbb{R}^{n} (in this case n = 2, but I assume that's fairly irrelevant), and I have the following norm:

\| f \|_{C^{1}}

I assume it has something to do with C^{1} maps, but I haven't come across it before.

Does anyone know what it is?
 
Physics news on Phys.org
Well, it might be this. Hope it helps!
 

Attachments

spamiam said:
Well, it might be this. Hope it helps!

Thanks for that. It's looking like my best bet at the moment.

I was sort of hoping that it would be some piece of common notation that I just hadn't come across, but it's not looking that way at the moment.
 
##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
When decomposing a representation ##\rho## of a finite group ##G## into irreducible representations, we can find the number of times the representation contains a particular irrep ##\rho_0## through the character inner product $$ \langle \chi, \chi_0\rangle = \frac{1}{|G|} \sum_{g\in G} \chi(g) \chi_0(g)^*$$ where ##\chi## and ##\chi_0## are the characters of ##\rho## and ##\rho_0##, respectively. Since all group elements in the same conjugacy class have the same characters, this may be...
Back
Top