Related papers: On Product Systems arising from Sum Systems

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

This is an attempt to model ambient space as a three-dimensional real affine space with a distinguished group of automorphisms containing the translations and acting freely and transitively on pairs consisting of a half-plane together with…

We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization…

The problem of the existence of non-pseudo-$\aleph_1$-compact $\mathbb R$-factorizable groups is studied. It is proved that any such group is submetrizable and has weight larger than $\omega_1$. Closely related results concerning the…

A Hilbert bimodule is a right Hilbert module X over a C*-algebra A together with a left action of A as adjointable operators on X. We consider families X = {X_s :s\in P} of Hilbert bimodules, indexed by a semigroup P, which are endowed with…

Gleason's theorem [A. Gleason, J. Math. Mech., \textbf{6}, 885 (1957)] is an important result in the foundations of quantum mechanics, where it justifies the Born rule as a mathematical consequence of the quantum formalism. Formally, it…

It is sometimes stated that Gleason's theorem prevents the construction of hidden-variable models for quantum entities described in a more than two-dimensional Hilbert space. In this paper however we explicitly construct a classical…

We present in the context of supersymmetric gauge theories an extension of the Weyl integration formula, first discovered by Robert Wendt, which applies to a class of non-connected Lie groups. This allows to count in a systematic way…

We describe the indecomposable components of the tangent bundle of the punctual Hilbert scheme of a smooth projective surface. As an application, we prove a recent conjecture about classification of products of punctual Hilbert schemes of…

It was proposed that the tensor product structure of the Hilbert space is uniquely determined by the Hamiltonian's spectrum, for most finite-dimensional cases satisfying certain conditions. I show that any such method would lead to…

We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained…

There has recently been much interest in the $C^*$-algebras of directed graphs. Here we consider product systems $E$ of directed graphs over semigroups and associated $C^*$-algebras $C^*(E)$ and $\mathcal{T}C^*(E)$ which generalise the…

Let $A$ and $B$ be finite subsets of $\mathbb{C}$ such that $|B|=C|A|$. We show the following variant of the sum product phenomenon: If $|AB|<\alpha|A|$ and $\alpha \ll \log |A|$, then $|kA+lB|\gg |A|^k|B|^l$. This is an application of a…

The first part of the paper is a brief overview of Hindman's finite sums theorem, its prehistory and a few of its further generalizations, and a modern technique used in proving these and similar results, which is based on idempotent…

We give a new proof the arithmetic Hilbert-Samuel theorem by using classical reductions in the theory of coherent sheaves, a direct proof in the case of the projective space and the conservation of some numerical invariants, called…

We present several results related to statistics for elliptic curves over a finite field $\mathbb{F}_p$ as corollaries of a general theorem about averages of Euler products that we demonstrate. In this general framework, we can reprove…

The notion of multiplicity of a module first arose as consequence of Hilbert's work on commutative algebra, relating the dimension of rings with the degree of certain polynomials. For noncommutative rings, the notion of multiplicity first…

Ewens-Pitman's partition structure arises as a system of sampling consistent probability distributions on set partitions induced by the Pitman-Yor process. It is widely used in statistical applications, particularly in species sampling…

We introduce a new algebraic framework to describe gravitational scrambling, including the semiclassical limit of any out-of-time-order correlation function that is built out of operator insertions separated by approximately the scrambling…

The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…