Related papers: A Bochner Type Theorem for Inductive Limits of Gel…

Let $\Hn$ be the $(2n+1)$-dimensional Heisenberg group and $K$ a compact group of automorphisms of $\Hn$ such that $(K\ltimes \Hn,K)$ is a Gelfand pair. We prove that the Gelfand transform is a topological isomorphism between the space of…

In this paper we extend the 1/N expansion introduced in [1] to group field theories in arbitrary dimension and prove that only graphs corresponding to spheres S^D contribute to the leading order in the large N limit.

Induced representations of Brauer algebra $D_{f}(n)$ from $S_{f_{1}}\times S_{f_{2}}$ with $f_{1}+f_{2}=f$ are discussed. The induction coefficients (IDCs) or the outer-product reduction coefficients (ORCs) of $S_{f_{1}}\times…

The Shapley-Folkman theorem is a statement about the Minkowski sum of (non-convex) sets, expressing the closeness of the Minkowski sum to convexity in a quantitative manner. This paper establishes similar theorems for integrally convex…

Finite-energy topological spherically symmetrical solutions of Chiral Born-Infeld Theory are studied. Properties of these solution are obtained, and a possible physical interpretation is also given.

We extend a classical result by Derdzinski and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. The new conditions of the theorem include Codazzi tensors (i.e. closed 1-forms) as well…

Let $\Lambda_1$, $\Lambda_2$ be two discrete orbits under the linear action of a lattice $\Gamma<\mathrm{SL}_2(\mathbb{R})$ on the Euclidean plane. We prove a Siegel$-$Veech-type integral formula for the averages $$…

We bound the number of incidences between points and spheres in finite vector spaces by bounding the sum of the number of points in the pairwise intersections of the spheres. We obtain new incidence bounds that are interesting when the…

In this paper, we introduce, for a separable Banach spacea new notion of besselian paires and of besselian Schauder frames for which we prove for some fundamental results.

In this paper we study some Schrodinger-Poisson type systems on a bounded domain, with Dirichlet boundary condition on both the variables.

It is well known that the pair $(\mathcal{S}_n,\mathcal{S}_{n-1})$ is a Gelfand pair where $\mathcal{S}_n$ is the symmetric group on $n$ elements. In this paper, we prove that if $G$ is a finite group then $(G\wr \mathcal{S}_n, G\wr…

We study a diophantine property for translation surfaces, defined in term of saddle connections and inspired by the classical theorem of Khinchin. We prove that the same dichotomy holds as in Khinchin' result, then we deduce a sharp…

An explicit bilinear generating function for Meixner-Pollaczek polynomials is proved. This formula involves continuous dual Hahn polynomials, Meixner-Pollaczek functions, and non-polynomial $_3F_2$-hypergeometric functions that we consider…

Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…

The classical Szeg\"o theorem can be stated in terms of the sequence of model spaces. In this article, we are interested in the generalization of the Szeg\"o theorem in the case of the sequence of powers of finite Blaschke products.

We apply the recently introduced notion, due to Dyckerhoff, Kapranov and Schechtman, of $N$-spherical functors of stable infinity categories, which generalise spherical functors, to the setting of monoidal categories. We call an object…

We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…

We provide an inductive proof of Borchardt's theorem for calculating the permanent of a Cauchy matrix via the determinants of auxiliary matrices. This result has implications for antisymmetric products of interacting geminals (APIG), and…

Let E = K< y_1, ..., y_n > be the exterior algebra. The ``(cohomological) distinguished pairs" of a graded E-module M describe the growth of a minimal graded injective resolution of M. Roemer gave a duality theorem between the distinguished…

A Gelfand model for an algebra is a module given by a direct sum of irreducible submodules, with every isomorphism class of irreducible modules represented exactly once. We introduce the notion of a perfect model for a finite Coxeter group,…