# Why Analytic in the upper hald plane required for Kramers-Kronig relations?

I've been reviewing the contents after quite a while. Now, when I'm reading Kramers-Kronig relations, I see that everywhere it is stated that the complex function have to be analytic in the upper half of the plane.

My question is, will the Kramers-Kronig relation be invalid if the function is analytic everywhere? And if that is so, why the analyticity in the upper half plane is required?

Any link to appropriate texts is also appreciated.

• analytic everywhere implies analytic in upper half plane, so I'm not sure what the confusion is... seems like you're mixing up what is the special case (being analytic everywhere) and what is the general case (analytic in upper half plane) Aug 30 at 2:00