Related papers: Space-time covariance functions with compact suppo…
The covariant Poisson equation for Lie algebra-valued mappings defined in 3-dimensional Euclidean space is studied using functional analytic methods. Weighted covariant Sobolev spaces are defined and used to derive sufficient conditions for…
We construct a canonical formulation of general relativity for the case of a timelike foliation of spacetime. The formulation possesses explicit covariance with respect to Lorentz transformations in the tangent space. Applying the loop…
Let T be a random field invariant under the action of a compact group G We give conditions ensuring that independence of the random Fourier coefficients is equivalent to Gaussianity. As a consequence, in general it is not possible to…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
We study the compact support property for solutions of the following stochastic partial differential equations: $$\partial_t u = a^{ij}u_{x^ix^j}(t,x)+b^{i}u_{x^i}(t,x)+cu+h(t,x,u(t,x))\dot{F}(t,x),\quad (t,x)\in…
In its canonical formulation, general relativity is subject to gauge transformations that are equivalent to space-time coordinate changes of general covariance only when the gauge generators, given by the Hamiltonian and diffeomorphism…
Time evolution equations for dynamical systems can often be derived from generating functionals. Examples are Newton's equations of motion in classical dynamics which can be generated within the Lagrange or the Hamiltonian formalism. We…
We propose flexible Gaussian representations for conditional cumulative distribution functions and give a concave likelihood criterion for their estimation. Optimal representations satisfy the monotonicity property of conditional cumulative…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
We first characterize the image of the compactly supported smooth even functions under the q-Weinstein transform as a subspace of the Schwartz space. We then describe the space of smooth $L_{\alpha, q, a}^{2}$-functions whose q-Weinstein…
In a recent paper [1], it has been shown that negative norm states are indispensable for a fully covariant quantization of the minimally coupled scalar field in de Sitter space. Their presence, while leaving unchanged the physical content…
The longstanding issue of general covariance in effective models of quantum gravity is addressed, which arises when canonical quantum gravity leads to a semiclassical model described by an effective Hamiltonian constraint. In the context of…
We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as…
We give sufficient geometric conditions, not involving capacities, for a compact null set to be removable for the Sobolev functions on weighted $\mathbb R^n$, defined as the closure of smooth functions in the weighted Sobolev norm. Our…
Gaussian processes (GP) are attractive building blocks for many probabilistic models. Their drawbacks, however, are the rapidly increasing inference time and memory requirement alongside increasing data. The problem can be alleviated with…
Positive definite functions of compact support are widely used for radial basis function approximation as well as for estimation of spatial processes in geostatistics. Several constructions of such functions for ${\mathbb R}^d$ are based…
The prevalence of multivariate space-time data collected from monitoring networks and satellites, or generated from numerical models, has brought much attention to multivariate spatio-temporal statistical models, where the covariance…
We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with…
The models of spin systems defined on Euclidean space provide powerful machinery for studying a broad range of condensed matter phenomena. While the non-relativistic effective description is sufficient for most of the applications, it is…
We present solutions corresponding to rotational configurations in the recently proposed Geometric Scalar Gravity (GSG) theory. The solutions obtained here have the important property that the associated closed time-like curves are always…