What do the underbraces in the following equations mean?

 

Edited May 30, 201015 yr by Uri

I believe in this case it means something like "this also means/can be written as". Not entirely sure though.

In that context, that some term is equal to what is over the underbrace. Often they are used for general notes.

Yeah that's what I was thinking intially but thanks for confirming it to me guys.

Usually they're informative. For example, people will often write something like

 

[math]\underbrace{1+1+\dots+1}_{\text{n times}}[/math]

 

which represents

 

[math]\sum_{k=1}^n 1[/math]

 

I find that it's a nice way of continuing steps in a proof without having to stop the train of thought, as it allows you to elaborate on a certain point in, say, a chain of equalities as is in your case.

it seems like Plancherel s theorem you can exchange functions if f(x)=sigma(g(x)exp(ikx))

here you can exchange f and g while changing i to -i .