  Dallenbach layer is composed of an absorbing magnetic-dielectric layer
attached to a perfect electric conductor (PEC) sheet. Under linearity and time
invariance (LTI) assumptions Rozanov has established analytically a sum-rule
trade-off between the absorption efficacy over a predefined bandwidth and the
thickness of the layer, that is the so-called Rozanov bound. In recent years
several proposals have been introduced to bypass this bound by using non-LTI
absorbers. However, in practice, their implementation may be challenging. Here,
we expose additional hidden assumptions in Rozanov's derivation, and thus we
introduce several new sum rules for LTI layer absorbers that are not covered by
the original Rozanov's criterion, and give rise to more relaxed constraints on
the absorption limit. We then, demonstrate practical LTI designs of absorbing
thin layers that provide absorption beyond the Rozanov's bound. These designs
are based on the replacement of the original PEC boundary by various types of
penetrable impedance sheet.
