%0 Journal Article %T On variants of $H$-measures and compensated compactness %A Evgeny Yu. Panov %J Mathematics %D 2014 %I arXiv %X We introduce new variant of $H$-measures defined on spectra of general algebra of test symbols and derive the localization properties of such $H$-measures. Applications for the compensated compactness theory are given. In particular, we present new compensated compactness results for quadratic functionals in the case of general pseudo-differential constraints. The case of inhomogeneous second order differential constraints is also studied. %U http://arxiv.org/abs/1403.6345v1