0. Introduction We work over an algebraically closed field k of characteristic 0. 0.1. Statement. In this paper, we use techniques of toric geometry to reprove the following theorem: Theorem 0.1. Let X be a projective variety of finite type over k, and let Z ⊂ X be a proper closed subset. Let G ⊂ Aut k (Z ⊂ X) be a finite group. Then there is a G-equivariant modification r : X 1 → X such that X...

Maximum principles and uniform anti-maximum are a ubiquitous topic in PDE theory that is closely tied to the Krein--Rutman theorem kernel estimates for resolvents. We take up classical idea of Tak\'a\v{c} - prove (anti-)maximum an abstract operator theoretic framework combine it with recent ideas from eventually positive semigroups. This enables us derive necessary sufficient conditions very ge...

The classical Krein-Naimark formula establishes a one-to-one correspondence between the generalized resolvents of a closed symmetric operator in a Hilbert space and the class of Nevanlinna families in a parameter space. Recently it was shown by V.A. Derkach, S. Hassi, M.M. Malamud and H.S.V. de Snoo that these parameter families can be interpreted as so-called Weyl families of boundary relation...

We prove in this paper resolvent estimates for the boundary values of resolvents of selfadjoint operators on a Krein space: if H is a selfadjoint operator on a Krein space H, equipped with the Krein scalar product 〈·|·〉, A is the generator of a C0−group on H and I ⊂ R is an interval such that: 1) H admits a Borel functional calculus on I, 2) the spectral projection 1lI (H) is positive in the Kr...

Article history: Received 13 September 2016 Accepted 28 February 2017 Available online 6 March 2017 Communicated by E. Milman MSC: 35A15 35B40 35K55 47J10

This paper is concerned with the finite-time H∞ filtering problem for linear continuous timevarying systems with uncertain observations and L2-norm bounded noise. The design of finitetimeH∞ filter is equivalent to the problem that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive. The quadratic form is related to a Krein statespace model accor...