ar X iv : m at h - ph / 0 40 40 70 v 1 2 8 A pr 2 00 4 Spectral Theory of Time Dispersive and Dissipative Systems

ar X iv : m at h - ph / 0 40 40 70 v 2 1 6 D ec 2 00 4 Spectral Theory of Time Dispersive and Dissipative Systems

We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system – which we show is essentially ...

ar X iv : m at h - ph / 0 40 40 26 v 1 8 A pr 2 00 4 THE DE RHAM - HODGE - SKRYPNIK THEORY OF DELSARTE TRANSMUTATION OPERATORS IN MULTIDIMENSION AND ITS APPLICATIONS

Spectral properties od Delsarte transmutation operators are studied , their differential geometrical and topological structure in multidimension is analyzed, the relationships with De Rham-Hodge-Skrypnik theory of generalized differential complexes is stated.

ar X iv : m at h - ph / 0 40 40 06 v 1 2 A pr 2 00 4 Pure point spectrum for the time evolution of a periodically rank - N kicked Hamiltonian

We find the conditions under which the spectrum of the unitary time evolution operator for a periodically rank-N kicked system remains pure point. This stability result allows one to analyse the onset of, or lack of chaos in this class of quantum mechanical systems, extending the results for rank-1 systems produced by Combescure and others. This work includes a number of unitary theorems equiva...

ar X iv : m at h - ph / 0 60 70 40 v 1 2 0 Ju l 2 00 6 Invariant Form of BK - factorization and its Applications

ar X iv : 0 80 4 . 40 12 v 1 [ m at h . D G ] 2 4 A pr 2 00 8 WHICH AMBIENT SPACES ADMIT

We give simple conditions on an ambient manifold that are necessary and sufficient for isoperimetric inequalities to hold.