Related papers: Powers of Brownian Green Potentials

In this article, a sublinear expectation induced by $G$-expectation is introduced, which is called $G$-evaluation for convenience. As an application, we prove that any $\xi\in L^\beta_G(\Omega_T)$ with some $\beta>1$ the decomposition…

The Green functions of the partial differential operators of even order acting on smooth sections of a vector bundle over a Riemannian manifold are investigated via the heat kernel methods. We study the resolvent of a special class of…

An interesting feature of some open superstring models in $D < 10$ is the simultaneous presence, in the spectrum, of gauge fields and of a number of antisymmetric tensor fields. In these cases the Green-Schwarz mechanism can (and does) take…

The critical behavior of the $(n+1)$-states Potts model in $d$-dimensions is studied with functional renormalization group techniques. We devise a general method to derive $\beta$-functions for continuos values of $d$ and $n$ and we write…

In linear perturbation theory, all information about the growth of structure is contained in the Green's function, or equivalently, transfer function. These functions are generally computed using numerical codes or by phenomenological…

We establish the following quantitative form of the Green--Tao theorem: if a set $\mathcal{A}$ of relative density $\delta$ within the primes up to $N$ contains no nontrivial arithmetic progressions of length $k\geq 4$, then $\delta\ll…

In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…

We study the Green function of the Poisson equation in two, three and four dimensions. The solution g of the equation nabla^2 g(x - x') = delta^(D)(x - x'), where x and x are D-dimensional position vectors, is customarily expanded into…

We use the mirror coupling of Brownian motion to show that under a $\beta\in (0,1)$-dependent Kato type assumption (which is satisfied under a suitable $L^q$-assumption on the electro-magnetic potential, where $q$ depends on $\beta$ and the…

Using a path integral approach and bosonization, we calculate the low energy asymptotics of the one particle Green's function for a ``magnetically incoherent'' one dimensional strongly interacting electron gas at temperatures much greater…

We study the connection between weighted Bergman kernel and Green's function on a domain W lying in C for which the Green's function exists.

We show for $n,k\geq1$, and an $n$-dimensional complex vector space $V$ that if an element $A\in\text{End}(V)[[z]]$ has constant term similar to a Jordan block, then there exists a polynomial gauge transformation $g$ such that the first $k$…

Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…

Relativistic mean field theory is formulated with the Green's function method in coordinate space to investigate the single-particle bound states and resonant states on the same footing. Taking the density of states for free particle as a…

Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…

Beta-decay properties of neutron-rich Zr and Mo isotopes are investigated within a microscopic theoretical approach based on the proton-neutron quasiparticle random-phase approximation. The underlying mean field is described…

In the theory of $g_\alpha$-potentials on a domain $D\subset\mathbb R^n$, $n\geqslant2$, $g_\alpha$ being the $\alpha$-Green kernel associated with the $\alpha$-Riesz kernel $|x-y|^{\alpha-n}$ of order $\alpha\in(0,n)$, $\alpha\leqslant2$,…

Consider operators of the form $L^{\gamma V}:=\Delta +\gamma V$ in a bounded Lipschitz domain $\Omega\subset \mathbb{R}^N$. Assume that $V\in C^1(\Omega)$ satisfies $|V(x)| \leq \bar a \,\mathrm{distance}\,(x,\partial\Omega)^{-2}$ for every…

We consider radiative \beta--decay of the neutron in heavy baryon chiral perturbation theory, with an extension including explicit \Delta degrees of freedom. We compute the photon energy spectrum as well as the photon polarization; both…

In this paper we prove that on a CR manifold of hypersurface type that satisfies the weak $Y(q)$ condition, the complex Green operator $G_q$ is exactly (globally) regular if and only if the Szeg\"o projections $S_{q-1}, S_q$ and a third…