Krein-Hermitian Hamiltonians, i.e., Hamiltonians Hermitian with respect to an indefinite inner product, have emerged as important class of non-Hermitian in physics, encompassing both single-particle bosonic Bogoliubov--de Gennes (BdG) and so-called ``$PT$-symmetric'' Hamiltonians. In particular, they attracted considerable scrutiny owing the recent surge interest for boson topology. Motivated b...

We construct a class of exact commensurate and incommensurate standing wave (SW) solutions in a piecewise smooth analogue of the discrete non-linear Schrödinger (DNLS) model and present their linear stability analysis. In the case of the commensurate SW solutions the analysis reduces to the eigenvalue problem of a transfer matrix depending parametrically on the eigenfrequency. The spectrum of e...

A reference potential approach to the one-dimensional quantummechanical inverse problem is developed. All spectral characteristics of the system, including its discrete energy spectrum, the full energy dependence of the phase shift, and the Jost function, are expected to be known. The technically most complicated task in ascertaining the potential, solution of a relevant integral equation, has ...

Owing to their numerous merits, such as compact, autonomous and independence, the strapdown inertial navigation system (SINS) and celestial navigation system (CNS) can be used in marine applications. What is more, due to the complementary navigation information obtained from two different kinds of sensors, the accuracy of the SINS/CNS integrated navigation system can be enhanced availably. Thus...

Characterization of generalized Schur functions in terms of their Taylor coefficients was established by M. G. Krein and H. Langer in [14]. We establich a boundary analog of this characterization.

The paper contains a survey of known results on the structure J-symmetric operator algebras in Pontryagin and Krein spaces, as well representations groups *-algebras these spaces.

The recently investigated Hilbert-Krein and other positivity structures of the superspace are considered in the framework of superdistributions. These tools are applied to problems raised by the rigorous supersymmetric quantum field theory.

We generalize the well known characterizations of totally nonnegative and oscillatory matrices, due to F. R. Gantmacher, M. G. Krein, A. Whitney, C. Loewner, M. Gasca, and J. M. Peña to the case of an arbitrary complex semisimple Lie group.

We consider a singular Sturm-Liouville differential expression with an indefinite weight function and we show that the corresponding self-adjoint differential operator in a Krein space locally has the same spectral properties as a definitizable operator.