Related papers: Mahavier Products, Idempotent Relations, and Condi…

We generalize the concept of mutually unbiased bases (MUB) to measurements which are not necessarily described by rank one projectors. As such, these measurements can be a useful tool to study the long standing problem of the existence of…

We prove that for any free ergodic nonsingular nonamenable action \Gamma\ \actson (X,\mu) of all \Gamma\ in a large class of groups including all hyperbolic groups, the associated group measure space factor $L^\infty(X) \rtimes \Gamma$ has…

For a finite, positive, Borel measure $\mu$ on $(0,1)$ we consider an infinite matrix $\Gamma_\mu$, related to the classical Hausdorff matrix defined by the same measure $\mu$, in the same algebraic way that the Hilbert matrix is related to…

We consider two inverse boundary value problems for the time-harmonic Maxwell equations in an infinite slab. Assuming that tangential boundary data for the electric and magnetic fields at a fixed frequency is available either on subsets of…

Maps between spaces of measures on measurable spaces $(X,\Sigma_X)$ and $(Y, \Sigma_Y)$ are treated as generalized functions between $X$ and $Y$.

We say that a list $\Lambda =\{ \lambda _{1},\ldots ,\lambda _{n}\}$ of complex numbers is realizable, if it is the spectrum of a nonnegative matrix $A$ (the realizing matrix). We say that $\Lambda $ is universally realizable if it is…

We demonstrate a relative solidity property for the product of a nonamenable biexact group with an arbitrary infinite group in the measure equivalence setting. Among other applications, we obtain the following unique product decomposition…

Metrizable spaces are studied in which every closed set is an $\alpha$-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of…

We generalise a result of Sawyer to show the following: For each y\in R^p and w\in R^q let \Gamma(y,w) be a measurable d-dimensional surface in R^n. Under conditions on the number of parameters and smoothness assumptions, there exists a set…

We prove higher summability and regularity of \Gamma(f) for functions f in spaces satisfying the Bakry-\'Emery condition BE(K,\infty). As a byproduct, we obtain various equivalent weak formulations of BE(K,N) and we prove the…

Suppose that $N$ is a smooth manifold with a smooth Riemannian metric $g_0$, and that $\Gamma$ is a smooth submanifold of $N$. This paper proves that for a generic (in the sense of Baire category) smooth metric $g$ conformal to $g_0$, if…

For a countably infinite group $\Gamma$, let $\mathcal{W}_\Gamma$ denote the space of all weak equivalence classes of measure-preserving actions of $\Gamma$ on atomless standard probability spaces, equipped with the compact metrizable…

We consider the question whether, given a countable system of lattices $(\Gamma_j)_{j \in J}$ in a locally compact abelian group $G$, there exists a sequence of functions $(g_j)_{j \in J}$ such that the resulting generalized shift-invariant…

The notion of $\ast$-idempotent measure is a modification of the notion of idempotent measure defined for every triangular norm $\ast$. We prove existence and uniqueness of invariant $\ast$-idempotent measures for iterated function systems…

Consider two free measure preserving group actions $\Gamma \actson (X, \mu), \Delta \actson (X, \mu)$, and a measure preserving action $\Delta \actson^a (Z, \nu)$ where $(X, \mu), (Z, \nu)$ are standard probability spaces. We show how to…

We study a new bi-Lipschitz invariant \lambda(M) of a metric space M; its finiteness means that Lipschitz functions on an arbitrary subset of M can be linearly extended to functions on M whose Lipschitz constants are enlarged by a factor…

A novel general framework for the study of $\Gamma$-convergence of functionals defined over pairs of measures and energy-measures is introduced. This theory allows us to identify the $\Gamma$-limit of these kind of functionals by knowing…

We introduce bounded category forcing axioms for well-behaved classes $\Gamma$. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe $H_{\lambda_\Gamma^+}$ modulo…

$\Gamma$-structures are weak forms of multiplications on closed oriented manifolds. As shown by Hopf the rational cohomology algebras of manifolds admitting $\Gamma$-structures are free over odd degree generators. We prove that this…

Let $\Gamma_g$ be a surface group of genus $g\geq 2$. It is known that the canonical central extension $\tilde{\Gamma}_g$ and the direct product $\Gamma_g\times \mathbb{Z}$ are quasi-isometric. It is also easy to see that they are measure…