The "Krein" regularization method of quantum field theory is studied, inspired by the Krein space quantization and metric fluctuations. It was previously considered in one-loop approximation, this paper generalized to all orders perturbation theory. We directly recover physical results obtained starting from standard QFT imposing renormalization conditions. By applying our approach curved space...

We solve the inverse problem from the spectral measure and the inverse three-spectra problem for the class of singular Krein strings on a finite interval with trace class resolvents. In particular, this includes a complete description of all possible spectral measures and three (Dirichlet) spectra associated with this class of Krein strings. The solutions of these inverse problems are obtained ...

In this note we give a Krein space interpretation of the celebrated Kalman-Yakubovich-Popov (KYP) Lemma by introducing state-space models driven by inputs that lie in an indeenite-metric space. Such state-space models can be considered as generalizations of standard stochastic state-space models driven by stationary stochastic processes (that lie in a deenite, or so-called Hilbert, space). In t...

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the re...

A criterion for the numerical range of a linear operator acting in a Krein space to be a two-component hyperbolical disc is given, using the concept of support function. A characterization of the Krein space numerical range as a union of hyperbolical discs is obtained by a reduction to the two-dimensional case. We revisit a famous result of Ando concerning the inclusion relation W (A) ⊆ W (B) o...

We present a simple proof of the Markov–Krein identity for distributions of means of linear functionals of the Dirichlet process and its various generalizations. The key idea is to use the representation of the Dirichlet process as the normalized gamma process and fundamental properties of gamma processes. Bibliography: 19 titles. 1. Introduction: Dirichlet processes, gamma processes and the Ma...

Krein-de Branges spectral theory establishes a correspondence between the class of differential operators called canonical Hamiltonian systems and measures on real line with finite Poisson integral. We further develop this area by giving description whose have logarithmic integral converging over line. This result can be viewed as version classical Szego theorem in polynomials orthogonal unit c...

This paper presents analogs, for certain mixed boundary-value problems, of the spectral and oscillatory properties exhibited by classical Sturm-Liouville systems. ‘l’he usual analysis of the Sturm-Liouville eigenvalue problem is based on special ad hoc methods. In contrast, Gantmacher and Krein [3; see also references therein] showed that these fundamental spectral properties are direct consequ...