The isospectrality problem is studied for the operator of the spherical hydromagnetic α−dynamo. It is shown that this operator is formally pseudo-Hermitian (J−symmetric) and lives in a Krein space. Based on the J−symmetry, an operator intertwining Ansatz with first-order differential intertwining operators is tested for its compatibility with the structure of the α−dynamo operator matrix. An in...

Flutter of an elastic body of revolution spinning about its axis of symmetry is prohibited in the subcritical spinning speed range by the Krein theorem for the Hamiltonian perturbations. Indefinite damping creates conical domains of the subcritical flutter (subcritical parametric resonance) bifurcating into the pockets of two Whitney’s umbrellas when non-conservative positional forces are addit...

It is proven that in indefinite metric quantum field theory there exists a dense set of analytic vectors for the generator of the one parameter group of x0–x1 velocity transformations. This makes it possible to define complex velocity transformations also for the indefinite metric case. In combination with the results of Bros – Epstein – Moschella [12], proving Bisognano–Wichmann (BW) analytici...

This paper investigates the existence of positive solutions for a class of boundary value problems (BVP) of fractional impulsive differential equations and presents a number of new results. First, by constructing a novel transformation, the considered impulsive system is convert into a continuous system. Second, using a specially constructed cone, the Krein-Rutman theorem, topological degree th...

It is proved that a discrete group G is amenable if and only if for every unitary representation of G in an infinite-dimensional Hilbert space H the maximal uniform compactification of the unit sphere SH has a G-fixed point, that is, the pair (SH, G) has the concentration property in the sense of Milman. Consequently, the maximal U(H)equivariant compactification of the sphere in a Hilbert space...

In this article we introduce the notion of J-Parseval fusion frames in a Krein space K and characterize 1-uniform J-Parseval fusion frames with ζ = √ 2. We provide some results regarding construction of new J-tight fusion frame from given J-tight fusion frames. We also characterize an uniformly J-definite subspace of a Krein space K in terms of J-fusion frame. Finally we generalize the fundamen...

We consider non-conservative positive semigroups and obtain necessary sufficient conditions for uniform exponential contraction in weighted total variation norm. This ensures the existence of Perron eigenelements provides quantitative estimates spectral gap, complementing Krein–Rutman theorems generalizing probabilistic approaches. The proof is based on a non-homogenous h $h$ -transform semigro...

This is the last in a series of papers in which we generalized the Tannaka-Krein duality to compact groupoids. In [A1] we studied the representation theory of compact groupoids. In particular, we showed that irreducible representations have finite dimensional fibres. We also proved the Schur’s lemma, Gelfand-Raikov theorem and Peter-Weyl theorem for compact groupoids. In [A2] we studied the Fou...

The Bernstein approximation problem is to determine whether or not the space of all polynomials is dense in a given weighted C0-space on the real line. A theorem of de Branges characterizes non-density by existence of an entire function of Krein class being related with the weight in a certain way. An analogous result holds true for weighted sup-norm approximation by entire functions of exponen...

where p(t) and q(t) are real-valued functions and p(t) 6= 0 for any t ∈ R. In what follows we assume that a(t), b(t), and c(t) satisfy the periodicity conditions a(t+ T ) = a(t), b(t+ T ) = b(t), c(t+ T ) = c(t), t ∈ R. The system (2) (or (3)) is said to be stable if all solutions are bounded on R, unstable if all nontrivial solutions are unbounded on R, and conditionally stable if there exits ...