We give a representation of the Gamma subordinator as a Krein functional of Brownian motion, using the known representations for stable subordinators and Esscher transforms. In particular, we have obtained Krein representations of the subordinators which govern the two parameter Poisson-Dirichlet family of distributions [23].

Abstract John’s fundamental theorem characterizing the largest volume ellipsoid contained in a convex body $K$ $\mathbb{R}^{d}$ has seen several generalizations and extensions. One direction, initiated by V. Milman is to replace ellipsoids positions (affine images) of another $L$. Another, more recent direction consider logarithmically concave functions on instead bodies: we designate some spec...

We give conditions for the Mayer-Vietoris property to hold for the algebraic K-theory of blow-up squares of toric varieties and schemes, using the theory of monoid schemes. These conditions are used to relate algebraic K-theory to topological cyclic homology in characteristic p. To achieve our goals, we develop many notions for monoid schemes based on classical algebraic geometry, such as separ...

In this paper is introduced a new type of generalization of metric spaces called $S_b$ metric space. For this new kind of spaces it has been proved a common fixed point theorem for four mappings which satisfy generalized contractive condition. We also present example to confirm our theorem.

A consequence of the celebrated Dvoretzky–Milman theorem is a strong law large numbers for d-dimensional random projections n-dimensional cube. It shows that, with respect to Hausdorff distance, uniform projection cube [−1/n,+1/n]n onto Rd converges almost surely centered Euclidean ball radius 2/π, as n→∞. We start by providing an alternative proof this via Artstein–Vitale compact sets. Then, e...

We introduce a relative index for a pair of dissipative operators in a von Neumann algebra of finite type and prove an analog of the Birman-Schwinger principle in this setting. As an application of this result, revisiting the Birman-Krein formula in the abstract scattering theory, we represent the de la Harpe-Skandalis determinant of the characteristic function of dissipative operators in the a...

Fundamental problems of quantum field theory related to the representation problem of canonical commutation relations are discussed within a gauge field version of a van Hove-type model. The Coulomb field generated by a static charge distribution is described as a formal superposition of time-like pseudo-photons in Fock space with a Krein structure. In this context, a generalization of operator...