Related papers: The Klain approach to zonal valuations

Starting from the observation that in Yang-Mills theory the Schroedinger state functional in the momentum representation is not gauge invariant, we investigate the reversed question: Which are the representations for the operators of a…

We establish a q-generalization of Gordon's theorem that the space of diagonal coinvariants has a quotient identified with a perfect representation of the rational double affine Hecke algebra. It leads to a simple proof of his theorem and…

We use categorical method and birational geometry to study moduli spaces of quiver representations. From certain "representable" functor, we construct a birational transformation from the moduli space of representations of one quiver to…

We study the so-called integral means spectrum for univalent functions on the unit disk. Using an inequality of Prawitz (generalizing the classical area theorem of Gronwall), we find -- by applying a Moebius mapping to lift the result to…

We study the space of generalized translation invariant valuations on a finite-dimensional vector space and construct a partial convolution which extends the convolution of smooth translation invariant valuations. Our main theorem is that…

In this note we present some generalized versions of the Krein-Rutman theorem for sectorial operators. They are formulated in a fashion that can be easily applied to elliptic operators. Another feature of these generalized versions is that…

In many computer vision and shape analysis tasks, practitioners are interested in learning from the shape of the object in an image, while disregarding the object's orientation. To this end, it is valuable to define a rotation-invariant…

An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…

We use Malliavin operators in order to prove quantitative stable limit theorems on the Wiener space, where the target distribution is given by a possibly multidimensional mixture of Gaussian distributions. Our findings refine and generalize…

This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the…

We consider the problem of coupling Galilean-invariant quantum field theories to a fixed spacetime. We propose that to do so, one couples to Newton-Cartan geometry and in addition imposes a one-form shift symmetry. This additional symmetry…

The notion of a valuation on convex bodies is very classical. The notion of a valuation on a class of functions was recently introduced and studied by M. Ludwig and others. We study an explicit relation between continuous valuations on…

We develop a theory of Valuation Hilbert Modules and prove a version of Beurling's theorem for these. Then we apply our version of Beurling's theorem to obtain complete descriptions of the closed invariant subspaces of a number of Hilbert…

We study real-valued valuations on the space of Lipschitz functions over the Euclidean unit sphere $S^{n-1}$. After introducing an appropriate notion of convergence, we show that continuous valuations are bounded on sets which are bounded…

This paper studies an analog of the classical Schwartz space $ \mathscr{S}(\mathbb{R}^N) $ in the framework of $ (k, a) $-deformed harmonic analysis associated with the $ (k, a) $-generalized Fourier transform $ \mathscr{F}_{k, a} $.…

We characterise modulation spaces by suitable Wiener estimates on the short-time Fourier transforms of the involved functions and distributions. We use the results to refine some formulae on periodic distributions with Lebesgue estimates on…

New universal invariant operators are introduced in a class of geometries which include the quaternionic structures and their generalisations as well as 4-dimensional conformal (spin) geometries. It is shown that, in a broad sense, all…

The derivation of zonal polynomials involves evaluating the integral \[ \exp\left( - \frac{1}{2} \operatorname{tr} D_{\beta} Q D_{l} Q \right) \] with respect to orthogonal matrices \(Q\), where \(D_{\beta}\) and \(D_{l}\) are diagonal…

We resort to the concept of turns to provide a geometrical representation of the action of any lossless multilayer, which can be considered as the analogous in the unit disk to the sliding vectors in Euclidean geometry. This construction…

Valuations on the space of finite-valued convex functions on $\mathbb{C}^n$ that are continuous, dually epi-translation invariant, as well as $\mathrm{U}(n)$-invariant are completely classified. It is shown that the space of these…