相关论文: Inside Out: Meet The Operators Inside The Horizon

We study the boundedness of some sublinear operators on weighted Morrey spaces under certain size conditions. These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator,…

We study a correspondence between gravitational shockwave geometry and its fluid description near a Rindler horizon in Minkowski spacetime. Utilizing the Petrov classification that describes algebraic symmetries for Lorentzian spaces, we…

We consider the current operators of one dimensional integrable models. These operators describe the flow of the conserved charges of the models, and they play a central role in Generalized Hydrodynamics. We present the key statements about…

This work presents a tensorial approach to constructing data-driven reduced-order models corresponding to semi-discrete partial differential equations with canonical Hamiltonian structure. By expressing parameter-varying operators with…

We give a generalization of the Hodge operator to spaces $(V,h)$ endowed with a hermitian or symmetric bilinear form $h$ over arbitrary fields, including the characteristic two case. Suitable exterior powers of $V$ become free modules over…

The goal of this paper is to derive estimates of eigenvalue moments for Dirichlet Laplacians and Schr\"odinger operators in regions having infinite cusps which are geometrically nontrivial being either curved or twisted; we are going to…

Realizations of the holographic correspondence in String/M theory typically involve spacetimes of the form $AdS \times Y$ where $Y$ is some internal space which geometrizes an internal symmetry of the dual field theory, hereafter referred…

Cosmic horizons arise in general relativity in the context of black holes and in certain cosmologies. Classically, regions beyond a horizon are inaccessible to causal observers. However, quantum mechanical correlations may exist across…

The analysis of branching problems for restriction of representations brings the concept of symmetry breaking transform and holographic transform. Symmetry breaking operators decrease the number of variables in geometric models, whereas…

A method based off of operator consideration for solving the time evolution of a wave function is developed. The method is applied to free space, constant force and harmonic oscillator potentials where general solutions are derived for the…

We apply the ultrarelativistic boosting procedure to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface, by exploiting the picture of…

We give an algorithm to write down all conformally invariant differential operators acting between scalar functions on Minkowski space. All operators of order k are nonlinear and are functions on a finite family of functionally independent…

We address the general question of how to reconstruct the field content of a quantum field theory from a given scattering theory in the context of the form factor program. For the $SU(3)_2$-homogeneous Sine-Gordon model we construct…

This paper concerns the random source problems for the time-harmonic acoustic and elastic wave equations in two and three dimensions. The goal is to determine the compactly supported external force from the radiated wave field measured in a…

In this note, we describe how the study of backgrounds for general quantum systems can be formulated in terms of the representation theory of abstract $C^*$ algebras. We illustrate our general framework through two example systems:…

We study operator algebras arising from monomial ideals in the ring of polynomials in noncommuting variables, through the apparatus of subproduct systems and C*-correspondences. We provide a full comparison amongst the related operator…

With a densely defined symmetric semi-bounded operator of nonzero defect indexes $L_0$ in a separable Hilbert space ${\cal H}$ we associate a topological space $\Omega_{L_0}$ ({\it wave spectrum}) constructed from the reachable sets of a…

We define and study Toeplitz operators in the space of Herglotz solutions of the Helmholtz equation in $R^d$. As the most traditional definition of Toeplitz operators via Bergman-type projection is not available here, we use an approach…

We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature…

In a spacetime $(\mathcal{M},g)$, a horizon is a null hypersurface where the deformation tensor $\mathcal{K}:=\pounds_{\eta}g$ of a null and tangent vector $\eta$ satisfies certain restrictions. In this work, we develop a formalism to study…