相关论文: A general correspondence between Dirichlet forms a…

Based on previous works, in this article we systematically analyze the implications of the explicit normal modes of a probe scalar sector in a BTZ background with a Dirichlet wall, in an asymptotically AdS-background. This is a…

We present the theory of the Dirichlet problem for nonlocal operators which are the generators of general pure-jump symmetric L\'evy processes whose L\'evy measures need not be absolutely continuous. We establish basic facts about the…

We establish an integral representation for the Dirichlet generating function of the coefficients of Euler's pentagonal number theorem. The Bromwich-type integral enables analytic continuation to the entire complex plane, filling a gap in…

If $U$ is a $C^{\infty}$ function with compact support in the plane, we let $u$ be its restriction to the unit circle $\mathbb{S}$, and denote by $U_i,\,U_e$ the harmonic extensions of $u$ respectively in the interior and the exterior of…

The Quillen-Bismut-Freed construction associates a determinant line bundle with connection to an infinite dimensional super vector bundle with a family of Dirac-type operators. We define the regularized first Chern form of the infinite…

In this paper, we shall first establish the theory of bivariate Revuz correspondence of positive additive functionals under a semi-Dirichlet form, which is associated with a right Markov process $X$ satisfying the sector condition but…

This paper presents a new perspective on unifying all fundamental interactions--gravitational, electromagnetic, weak and strong--based on stochastic processes rather than conventional quantum mechanics. Earlier work by Nelson, Kac and…

We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima's ergodic theorem for the harmonic functions in the domain of the $ L^{p} $ generator. Secondly we prove analogues of Yau's and Karp's…

Mean-field theory is an approximation replacing an extended system by a few variables. For depinning of elastic manifolds, these are the position of its center of mass $u$, and the statistics of the forces $F(u)$. There are two proposals to…

Consider any Dirichlet series sum a_n/n^z with nonnegative coefficients a_n and finite sum function f(z)=f(x+iy) when x is greater than 1. Denoting the partial sum a_1+...+a_N by s_N, the paper gives the following necessary and sufficient…

We reprove the essential self-adjointness of the Dirichlet operators of Dirchlet forms for infinite particle systems with superstable and sub-exponentially decreasing interactions.

We discuss de Branges-Rovnyak spaces $\mathcal H(b)$ generated by nonextreme and rational functions $b$ and local Dirichlet spaces of order $m$ introduced in [6]. In [6] the authors characterized nonextreme $b$ for which the operator…

An approach is presented to resolve key paradoxes in black hole physics through the application of complex Riemannian spacetime. We extend the Schwarzschild metric into the complex domain, employing contour integration techniques to remove…

The quantum action principle of renormalisation theory is applied to the antibracket-antifield formalism for Hamiltonian systems. General results on the local BRST cohomology allow one to prove that the anomalies appear in the time…

Ferguson's Dirichlet process plays an important role in nonparametric Bayesian inference. Let $P_a$ be the Dirichlet process in $\mathbb{R}$ with a base probability measure $H$ and a concentration parameter $a>0.$ In this paper, we show…

We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…

A particular consequence of the famous Carleson-Hunt theorem is that the Taylor series expansions of bounded holomorphic functions on the open unit disk converge almost everywhere on the boundary, whereas on single points the convergence…

Recently it was demonstrated that by adding to the Einstein-Hilbert action a series in powers of the curvature invariants with specially chosen coefficients one can obtain a theory of gravity which has spherically symmetric solutions…

The local, covariant, continuous, anticommuting and nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for all the fields of a (0 + 1)-dimensional spinning relativistic particle are obtained in the framework…

We consider the dynamics of a four-form field $\tilde {w} $, treating it as a distinct physical degree of freedom, independent of the metric. The equations of motion are derived from an action which, besides having the standard…