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...

In this paper, we consider two new uniqueness results for fuzzy fractional differential equations (FFDEs) involving Riemann-Liouville generalized H-differentiability with the Nagumo-type condition and the Krasnoselskii-Krein-type condition. To this purpose, the equivalent integral forms of FFDEs are determined and then these are used to study the convergence of the Picard successive approximati...

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...

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 ...

We present the current state of the art concerning the global and local Markov inequalities in the complex plane. This paper is based on a talk given during the Workshop on Multivariate Approximation in honor of Prof. Len Bos 60th birthday, and rests on articles [4], [5] and [6]. Our research is inspired by papers by Bos and Milman where global and local Markov inequalities are compared in the ...