Related papers: Bi-Free Probability Theory and Reflection Positivi…
A simple condition is given that is sufficient to determine whether a measure that is absolutely continuous with respect to a Gau{\ss}ian measure on the space of distributions is reflection positive. It readily generalises conventional…
A simple construction of Euclidean invariant and reflection positive measures on the cylindrical compactification is performed under a weaker hypothesis than has recently been obtained. Moreover, the results are extended to the case when…
The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free multiarrangements are…
We show how several useful properties of Ind-constructions in $\infty$-categories extend to arbitrary free colimit completion constructions.
Modifications of the authors' previously-published, generalized, lumped-element, reflectionless filter topologies are presented which remove the original constraints on the relative values of its prototype parameters. Thus, any transfer…
We define reflective numbers and their iterative summations. We provide classification of reflective numbers based on their iterative cyclical limits.
Reflection positivity originates from one of the Osterwalder-Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in…
We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated…
We give a construction of two-sided invariant metrics on free products (possibly with amalgamation) of groups with two-sided invariant metrics and, under certain conditions, on HNN extensions of such groups. Our approach is similar to the…
In this paper we will study an important but rather technical result which is called The Reduction Property. The result tells us how much arithmetical conservation there is between two arithmetical theories. Both theories essentially speak…
We consider a generalisation of the Majid's mirror product of a Hopf algebra H, when one of the components of the product is replaced by a twist. This leads to a new "twisted mirror product" construction for cocycle bicrossproduct Hopf…
We introduce a generalization of stationary set reflection which we call "filter reflection", and show it is compatible with the axiom of constructibility as well as with strong forcing axioms. We prove the independence of filter reflection…
The concept of reflection positivity has its origins in the work of Osterwalder--Schrader on constructive quantum field theory. It is a fundamental tool to construct a relativistic quantum field theory as a unitary representation of the…
Let $\k$ be a field, and let $A$ and $B$ be connected $\N$-graded $\k$-algebras. The algebra $A$ is said to be a graded right-free extension of $B$ provided there is a surjective graded algebra morphism $\pi: A \to B$ such that $\ker\pi$ is…
Negative refraction is known to occur in materials that simultaneously possess a negative electric permittivity and magnetic permeability; hence they are termed negative index materials. However, there are no known natural materials that…
Let $\mathcal{A} = \mathcal{A}(W)$ be the reflection arrangement of the finite complex reflection group $W$. By Terao's famous theorem, the arrangement $\mathcal{A}$ is free. In this paper we classify all reflection arrangements which…
Several characterizations are given for a square matrix that can be written as the product of two positive (semidefinite) projections. Based on one of these characterizations, and the theory of alternating projections, a Matlab program is…
We study the recurrence of the product of n functions, each of which satisfies the same recurrence relation.
We find a necessary and sufficient condition for the existence of the tensor product of modules over a Lie conformal algebra. We provide two algebraic constructions of the tensor product. We show the relation between tensor product and…
This paper is devoted to the proof of the property of order separability for free product of free groups with maximal cyclic amalgamated subgroups.