Related papers: p-dimensional cones and applications
The curvature tensor of a pseudo-Riemannian metric, and its covariant derivatives, satisfy certain identities that hold on any manifold of dimension less or equal than $n$. In this paper, we re-elaborate recent results by…
We derive novel concentration inequalities for the operator norm of the sum of self-adjoint operators that do not explicitly depend on the underlying dimension of the operator, but rather an intrinsic notion of it. Our analysis leads to…
One of the key ingredients of A. Connes' noncommutative geometry is a generalized Dirac operator which induces a metric(Connes' distance) on the state space. We generalize such a Dirac operator devised by A. Dimakis et al, whose Connes'…
Grassmann angles improve upon similar concepts of angle between subspaces that measure volume contraction in orthogonal projections, working for real or complex subspaces, and being more efficient when dimensions are different. Their…
The investigation of the dimension of Bergman spaces has long been a central topic in several complex variables, uncovering profound connections with potential theory and function theory since the pioneering work of Carleson, Wiegerinck,…
Let $H=H_+\oplus H_-$ be a fixed orthogonal decomposition of the complex Hilbert space $H$ in two infinite dimensional subspaces. We study the geometry of the set $P^p$ of selfadjoint projections in the Banach algebra $$ {\cal A}^p=\{A\in…
Let G be any reductive p-adic group. We discuss several conjectures, some of them new, that involve the representation theory and the geometry of G. At the heart of these conjectures are statements about the geometric structure of Bernstein…
The natural duality between "topological" and "regular," both considered as convergence space properties, extends naturally to p-regular convergence spaces, resulting in the new concept of a p-topological convergence space. Taking advantage…
We obtain the radial symmetry of the solution to a partially overdetermined boundary value problem in a convex cone in space forms by using the maximum principle for a suitable subharmonic function $P$ and integral identities. In dimension…
After defining generalizations of the notions of covariant derivatives and geodesics from Riemannian geometry for reductive Cartan geometries in general, various results for reductive Cartan geometries analogous to important elementary…
We prove sharp upper bounds for sums of eigenvalues (and other spectral functionals) of Laplace-like operators, including bi-Laplacian and fractional Laplacian. We show that among linear images of a highly symmetric domain, our spectral…
We consider $p$-orientations, which are defined to be orientations of $d$-regular graphs such that every vertex either has in-degree $p$ or out-degree $p$. These generalise the orientations considered in Jaeger's conjecture, where $d=4p+1$.…
We present recent advances in the analysis of nonlinear equations with singular operators and nonlinear optimization problems with constraints given by singular mappings. The results are obtained within the framework of $p$-regularity…
A topological model in three dimensions is proposed. It combines the Chern-Simons action with a BFK-model which was investigated recently by the authors of hep-th/9906146. The finiteness of the model to all orders of perturbation theory is…
We introduce and study a generalized concept of boundedness of a subset of a normed vector space with respect to a cone, which is defined as lower boundedness of the images of the underlying set through all the positive functionals of the…
The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of…
The Fibonacci cube $\Gamma_n$ is the subgraph of the hypercube $Q_n$ induced by vertices with no consecutive $1$s. Recently Jianxin Wei and Yujun Yang introduced a one parameter generalization, Fibonacci $p$-cubes $\Gamma_n^p$, which are…
The Kalb-Ramond action, derived for interacting strings through an action-at-a-distance force, is generalized to the case of interacting p-dimensional objects (p-branes) in D-dimensional space-time. The open p-brane version of the theory is…
We give explicit generators for ideals of two classes of subspace arrangements embedded in certain reflection arrangements, generalizing results of Li-Li and Kleitman-Lovasz. We also give minimal generators for the ideals of arrangements…
We investigate recursive properties of certain p-adic Whittaker functions (of which representation densities of quadratic forms are special values). The proven relations can be used to compute them explicitly in arbitrary dimensions,…