The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

The operator e−tA and the heat trace Tr e−tA, for t > 0, are investigated in the case when A is an elliptic differential operator on a manifold with conical singularities. Under a certain spectral condition (parameter–ellipticity) we obtain a full asymptotic expansion in t of the heat trace as t → 0+. As in the smooth compact case, the problem is reduced to the investigation of the resolvent (A...

We consider linear boundary value problems for higher-order parameter-elliptic equations, where the data do not belong to classical trace spaces. employ a class of Sobolev spaces mixed smoothness that admits generalized with values in Besov negative order. prove unique solvability rough half-space and sufficiently smooth domains. As an application, we show operator related linearized Cahn–Hilli...

We use the theory of Berezin-Toeplitz operators Ma and Marinescu to study spaces holomorphic sections a prequantizing line bundle over compact K\"ahler manifolds under deformations complex structure. show that parallel transport in induced vector deformation space behaves like Toeplitz operator, compute its first coefficient. then this result establish semi-classical trace formula for quantizat...

Abstract Quantum entanglement breaking channels are a fundamental class of quantum operations; originally investigated for information theoretic reasons, their study has since grown to touch on many aspects science. Here we investigate the nullspace structures and derive pair related applications. We show that every operator space trace zero matrices is an channel. test mixed unitarity based co...