Related papers: Spacetime Harmonic Functions and Applications to M…
We present a new efficient numerical approach for representing anisotropic physical quantities and/or matrix elements defined on the Fermi surface of metallic materials. The method introduces a set of numerically calculated generalized…
We prove the Harnack inequality for antisymmetric $s$-harmonic functions, and more generally for solutions of fractional equations with zero-th order terms, in a general domain. This may be used in conjunction with the method of moving…
This paper proposes a new approach to construct high quality space-filling sample designs. First, we propose a novel technique to quantify the space-filling property and optimally trade-off uniformity and randomness in sample designs in…
In this paper, we investigate some properties on harmonic functions and solutions to Poisson equations. First, we will discuss the Lipschitz type spaces on harmonic functions. Secondly, we establish the Schwarz-Pick lemma for harmonic…
In \cite{PSMA}, Pal et al. introduced some weighted means and gave some related inequalities by using an approach for operator monotone functions. This paper discusses the construction of these weighted means in a simple and nice setting…
We develop a new regularization method for the stress-energy tensor and the two-point function of free quantum scalar fields propagating in cosmological spacetimes. We proceed by extending the adiabatic regularization scheme with the…
We introduce two new effective quantities for the study of comoving curvature perturbations $\zeta$: the space dependent effective sound speed (SESS) and the momentum dependent effective sound speed (MESS) . We use the SESS and the MESS to…
In this paper, we show a new relation between phase transition in one-dimensional Statistical Mechanics and the multiplicity of the dimension of the space of harmonic functions for an extension of the classical transfer operator. We…
We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case…
The well-known spatial integration schemes in molecular electronic structure theory, immune to cusps and point singularities of some kind at atomic positions, use a set of weighting functions to split the integrand into a sum of…
Infinite dimensional moment problems have a long history in diverse applied areas dealing with the analysis of complex systems but progress is hindered by the lack of a general understanding of the mathematical structure behind them.…
We use a transformation due to Bekenstein to relate the ADM and Bondi masses of asymptotically-flat solutions of the Einstein equations with, respectively, scalar sources and conformal-scalar sources. Although the conformal-scalar…
The subject of this thesis is the coupling of quantum fields to a classical gravitational background in a semiclassical fashion. It contains a thorough introduction into quantum field theory on curved spacetime with a focus on the…
We construct an algorithm to determine all stationary axi-symmetric solutions of 3-dimensional Einstein gravity with a minimally coupled self-interacting scalar field. We holographically renormalize the theory and evaluate then the on-shell…
Spaces of harmonic functions in upper half-space with controlled growth near the boundary are described in terms of multiresolution approximations. The results are applied to prove the law of the iterated logarithm for the oscillation of…
Violations of spacetime symmetries have recently been identified as promising signatures for physics underlying the Standard Model. The present talk gives an overview over various topics in this field: The motivations for spacetime-symmetry…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
A positive cosmological constant simplifies the asymptotics of forever expanding cosmological solutions of the Einstein equations. In this paper a general mathematical analysis on the level of formal power series is carried out for vacuum…
We study the problem of asymptotically flat bi-axially symmetric stationary solutions of the vacuum Einstein equations in $5$-dimensional spacetime. In this setting, the cross section of any connected component of the event horizon is a…
Matrix elements of spinor and principal series representations of the Lorentz group are studied in the basis of complex angular momentum (helicity basis). It is shown that matrix elements are expressed via hyperspherical functions…