Related papers: Orbital integrals on Lorentzian symmetric spaces

The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…

We construct harmonic functions in the quarter plane for discrete Laplace operators. In particular, the functions are conditioned to vanish on the boundary and the Laplacians admit coefficients associated with transition probabilities of…

The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…

Let X be a noncompact symmetric space of rank one and let h^1(X) be a local atomic Hardy space. We prove the boundedness from h^1(X) to L^1(X) and on h^1(X) of some classes of Fourier integral operators related to the wave equation…

An order four automorphism of a Lie algebra gives rise to an integrable system discussed by Terng. We show that solutions of this system may be identified with certain vertically harmonic twistor lifts of conformal maps of surfaces in a…

In the finite-dimensional setting, every Hermitian-symmetric space of compact type is a coadjoint orbit of a finite-dimensional Lie group. It is natural to ask whether every infinite-dimensional Hermitian-symmetric space of compact type,…

Let $X=X_1 \times X_2$ be a direct product of two rank-one Riemannian symmetric spaces of the noncompact type. We show that when at least one of the two spaces is isomorphic to a real hyperbolic space of odd dimension, the resolvent of the…

We study tools of the conformal bootstrap in simplifying limits, primarily a limit of large operator dimensions and small cross-ratios corresponding to non-relativistic physics in AdS. We show that T-channel conformal blocks give the…

We demonstrate the existence in the sense of sequences of solutions for some integro-differential type problems involving the drift term and the square of the Laplace operator, on the whole real line or on a finite interval with periodic…

Motivated by considerations of euclidean quantum gravity, we investigate a central question of spectral geometry, namely the question of reconstructability of compact Riemannian manifolds from the spectra of their Laplace operators. To this…

We consider Calderon -- Zygmund singular integral in the discrete half-space $h{\bf Z}^m_{+}$, where ${\bf Z}^m$ is entire lattice ($h>0$) in ${\bf R}^m$, and prove that the discrete singular integral operator is invertible in $L_2(h{\bf…

We introduce the notion of orbital L-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from the intrinsic interest,…

We prove the Plancherel formula for spherical Schwartz functions on a reductive symmetric space. Our starting point is an inversion formula for spherical smooth compactly supported functions. The latter formula was earlier obtained from the…

We prove pointwise bounds for $L^2$ eigenfunctions of the Laplace-Beltrami operator on locally symmetric spaces with $\mathbb{Q}$-rank one if the corresponding eigenvalues lie below the continuous part of the $L^2$ spectrum. Furthermore, we…

In this paper we prove Hessian and Laplacian comparison theorems for the Lorentzian distance function in a spacetime with sectional (or Ricci) curvature bounded by a certain function by means of a comparison criterion for Riccati equations.…

In this paper we investigate solvability of a partial integral equation in the space $L_2(\Omega\times\Omega),$ where $\Omega=[a,b]^\nu.$ We define a determinant for the partial integral equation as a continuous function on $\Omega$ and for…

The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity…

We derive an explicit formula for the Laplace-Beltrami operator on the orthogonal Stiefel manifold, viewed as a constraint submanifold of the Euclidean space of real matrices equipped with the Frobenius metric. Using the general framework…

A construction of integrable hamiltonian systems associated with different graded realizations of untwisted loop algebras is proposed. Such systems have the form of Euler - Arnold equations on orbits of loop algebras. The proof of…

Motivated by problems arising in the relative trace formula and arithmetic invariant theory we prove the existence of rational points on orbits arising from certain infinitesimal symmetric spaces. As an application, we prove analogous…