We consider the case of scattering by several obstacles in Rd for d?2. In this setting, absolutely continuous part Laplace operator ? with Dirichlet boundary conditions and free ?0 are unitarily equivalent. For suitable functions that decay sufficiently fast, we have difference g(?)?g(?0) is a trace-class its trace described Krein spectral shift function. article, study contribution to (and hen...

Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group SO0(1, 4) or Sp(2, 2) as an appealing substitute to the flat space-time Poincaré relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable f...

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In particular, special attention is paid to the periodic generalized Jacobi operators. Finally, the spectral properties of generalized Jacobi operators are applied to pr...

We show that several interesting problems in Rw filtering, quadratic game theory, and risk sensitive control and estimation follow as special cases of the Krein-space linear estimation theory developed in [l]. We show that a11 these problems can be cast into the problem of calculating the stationary point of certain second-order forms, and that by considering the appropriate state space models ...

The power spectrum of scalar field and space-time metric perturbations produced in the process of inflation of universe, have been presented in this paper by an alternative approach to field quantization namely, Krein space quantization [1, 2]. Auxiliary negative norm states, the modes of which do not interact with the physical world, have been utilized in this method. Presence of negative norm...

New unique characterization results for the potential V (x) in connection with Schrödinger operators on R and on the half-line [0,∞) are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schrödinger operators on the half-line with purely discrete spectra to arbitrary sp...