Related papers: Spherical Functions: The Spheres Vs. The Projectiv…

A complete system of differential invariants for equivalence of curves in the $n$-dimensional pseudo-euclidean space with respect to the action of each of the groups $K^n \lhd O(n,p,K)$, $K^n \lhd SO(n,p,K)$, $O(n,p,K)$, and $SO(n,p,K)$,…

This paper has been withdrawn and replaced by arXiv:1309.5035. In this paper we describe some examples of so called spherical functors between triangulated categories, which generalize the notion of a spherical object. We also give…

In this work we discuss the notion of observable - both quantum and classical - from a new point of view. In classical mechanics, an observable is represented as a function (measurable, continuous or smooth), whereas in (von Neumann's…

Let $R$ be a root system of type BC in $\mathfrak a=\mathbb R^r$ of general positive multiplicity. We introduce certain canonical weight function on $\mathbb R^r$ which in the case of symmetric domains corresponds to the integral kernel of…

The paper presents a new and simple range characterization for the spherical mean transform of functions supported in the unit ball in even dimensions. It complements the previous work of the same authors, where they solved an analogous…

We use the Hardy spaces for Fourier integral operators to obtain bounds for spherical maximal functions in $L^{p}(\mathbb{R}^{n})$, $n\geq2$, where the radii of the spheres are restricted to a compact interval in $(0,\infty)$. These bounds…

We study the $L^p$ norm of the orthogonal projection from the space of quaternion valued $L^2$ functions to the closed subspace of slice $L^2$ functions.

The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic…

A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…

This paper provides a survey of spherical designs and their applications, with a particular emphasis on the perspective of ``numerical analysis''. A set \(X_N\) of \(N\) points on the unit sphere \(\mathbb{S}^d\) is called a…

Let the metric space $\mathbb R^n \setminus \sim$ be the metric space of $n$-sized unordered tuples of real numbers. In the following, it will be shown that if a function $\varphi: \mathbb R^m \to \mathbb R^n \setminus \sim$ is continuous,…

We will show that for any $n\ge N$ points on the $N$-dimensional sphere $S^N$ there is a closed hemisphere which contains at least $\lfloor\frac{n+N+1}{2}\rfloor$ of these points. This bound is sharp and we will calculate the amount of sets…

It is shown that the Topological Massive and ``Self-dual'' theories, which are known to provide locally equivalent descriptions of spin 1 theories in 2+1 dimensions, have different global properties when formulated over topologically…

We describe the quantum sphere of Podle\'{s} for $c=0$ by means of a stereographic projection which is analogous to that which exhibits the classical sphere as a complex manifold. We show that the algebra of functions and the differential…

In this paper we show how the superquadratic functions can be used as a tool for researching other types of convex functions like $\phi $-convexity, strong-convexity and uniform convexity. We show how to use inequalities satisfied by…

We examine basis functions on momentum space for the three dimensional Euclidean Snyder algebra. We argue that the momentum space is isomorphic to the SO(3) group manifold, and that the basis functions span either one of two Hilbert spaces.…

There is a growing interest in developing covariance functions for processes on the surface of a sphere due to wide availability of data on the globe. Utilizing the one-to-one mapping between the Euclidean distance and the great circle…

In this paper we deal with the problem of recovering functions from their spherical mean transform $\mathcal{R}$, which integrates functions on circles in the plane, in case where the centers of the circles of integration are located on a…

In previous work we have shown that the (\theta->\infty)-limit of \phi^4_4-quantum field theory on noncommutative Moyal space is an exactly solvable matrix model. In this paper we translate these results to position space. We show that the…

Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least…