相关论文: Translation invariant valuations on quasi-concave …
We prove weak type inequalities for a large class of noncommutative square functions. In conjunction with BMO type estimates, interpolation and duality, we will obtain the corresponding equivalences in the whole Lp scale. The main novelty…
In [MT2] the Vafa-Witten theory of complex projective surfaces is lifted to oriented $\mathbb C^*$-equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in $t^{1/2}$ invariant under…
A semiclassical approach is used to obtain Lorentz covariant expressions for the form factors between the kink states of a quantum field theory with degenerate vacua. Implemented on a cylinder geometry it provides an estimate of the…
Combinatorial mixed valuations associated to translation-invariant valuations on polytopes are introduced. In contrast to the construction of mixed valuations via polarization, combinatorial mixed valuations reflect and often inherit…
We outline a cohomological treatment for multivalued (classical) action functionals. We point out that an application of Takens' theorem, after Zuckerman, Deligne and Freed, allows to conclude that multivalued functionals yield globally…
Translation-invariant noncommutative gauge theories are discussed in the setting of matrix modeled gauge theories. Using the matrix model formulation the explicit form of consistent anomalies and consistent Schwinger terms for…
A new class of continuous valuations on the space of convex functions on $\mathbb{R}^n$ is introduced. On smooth convex functions, they are defined for $i=0,\dots,n$ by \begin{equation*} u\mapsto \int_{\mathbb{R}^n} \zeta(u(x),x,\nabla…
We present elements of a theory of translation-invariant integration on finite dimensional vector spaces and on GL_n over a valuation field with local field as residue field. We then discuss the case of an arbitrary algebraic group. This…
In this paper, we introduce a generalized piecewise translation map on the Euclidean space. We provide a special case when this map is always of finite type. For a finite type map in this case, we form conjectures on the semi-continuity of…
Unimodal univariate distributions can be characterized as piecewise convex-concave cumulative distribution functions. In this note we transfer this shape constraint characterization to the quantile function. We show that this…
We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…
Determination of quasi-invariant generalized functions is important for a variety of problems in representation theory, notably character theory and restriction problems. In this note, we review some new and easy-to-use techniques to show…
A $\lambda$-translator is a surface in Euclidean space $\mathbb{R}^3$ whose Gauss curvature $K$ satisfies $K=\langle N, \vec{v} \rangle +\lambda$, where $N$ is the Gauss map, $\vec{v}$ is a fixed direction, and $\lambda \in \mathbb{R}$. In…
It is proved that the classical Laplace transform is a continuous valuation which is positively GL$(n)$ covariant and logarithmic translation covariant. Conversely, these properties turn out to be sufficient to characterize this transform.
We consider the noncommutative space-times with Lie-algebraic noncommutativity (e.g. $\kappa$-deformed Minkowski space). In the framework with classical fields we extend the $\star$-product in order to represent the noncommutative…
We study non-trivial translation-invariant probability measures on the space of entire functions of one complex variable. The existence (and even an abundance) of such measures was proven by Benjamin Weiss. Answering Weiss question, we find…
We study multivariate entire functions and polynomials with non-negative coefficients. A class of {\bf Strongly Log-Concave} entire functions, generalizing {\it Minkowski} volume polynomials, is introduced: an entire function $f$ in $m$…
If a real-valued function is continuous on a real interval and it takes on two different values, then it will also take any value in between those two, by the Intermediate Value Theorem. It is not immediately clear what would be a natural…
Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym theorem relative to a Gould-type integral of real…
We study topologically invariant means on $L^{\infty}(\mathbb{R})$, the set of all essentially bounded functions on the real line, and prove that invariance with respect to a single convolution operator is sufficient for a mean to be…