What is the application of Kramers-Kr?nig relations?

I know that this question is a little silly, but i want to know the application of kramers-Kr?nig relations for the permittivity of dielectric materials. Is the application of K-K relations to extract the values of real and imaginary parts of the permittivity or what?

Many applications exist, as the relations govern the behavior of such devices/materials in the frequency domain. Is there a particular application you're looking for?

The relations can be used to constrain the real and imaginary components of a dielectric, but can't be used on their own to obtain these parameters.

I would like to design a composite materials that have permittivity and permeability as a function of frequency as microwave absorbers. I saw in many publications the authors mention the Kramers-Kr?nig relations and when i read about these relations, i observed that they find a relation between the real and imaginary parts of any complex function, but i did not understood why the authors use it.

The author's probably use the relation to find an operating point where the material is lossy, and hence absorb. They could also use them to show a particular dispersion profile for a particular loss profile.

These equations for this application will govern things like, for example, absorption (S11) vs bandwidth.