Related papers: The null identities for boundary operators in the …
In this paper, with a fixed $p\in (1,+\infty)$ and a bounded domain $\Omega \subset \mathbb{R}^N$ whose boundary $\partial\Omega$ fulfills the $C^1$ regularity, we study a boundary value problem involving a nonlocal operator assigning to…
In this paper we obtain the weak type (1,1) boundedness of Calderon-Zygmund operators acting over operator-valued functions. Our main tools for its solution are a noncommutative form of Calderon-Zygmund decomposition in conjunction with a…
We present a numerical scheme to calculate fluctuation identities for exponential L\'evy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult…
We find new special physical operators of $W_3 -$gravity having non trivial ghost sectors. Some of these operators may be viewed as the liouville dressings of the energy operator of the Ising model coupled to {\it 2d~gravity} and this fills…
The Boutet de Monvel calculus of pseudo-differential boundary operators is generalised to the full scales of Besov and Triebel--Lizorkin spaces (though with finite integral exponents for the latter). The continuity and Fredholm properties…
We quantise canonical free-field zero modes $p$, $q$ on a half-plane $p>0$ both, for the Liouville field theory and its reduced Liouville particle dynamics. We describe the particle dynamics in detail, calculate one-point functions of…
Consider a bivariate Geometric random variable where the first component has parameter $p_1$ and the second parameter $p_2$. It is not possible to make the correlation between the marginals equal to -1. Here the properties of this minimum…
We derive explicit expressions for a specific subclass of Jackiw-Teitelboim (JT) gravity bilocal correlators, corresponding to degenerate Virasoro representations. On the disk, these degenerate correlators are structurally simple, and they…
We investigate the $\mathcal R$-boundedness of operator families belonging to the Boutet de Monvel calculus. In particular, we show that weakly and strongly parameter-dependent Green operators of nonpositive order are $\mathcal R$-bounded.…
We consider the 2D super Liouville gravity coupled to the minimal superconformal theory. We analyze the physical states in the theory and give the general form of the n-point correlation numbers on the sphere in terms of integrals over the…
We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green's identity for the nonlocal operator that recovers the classical boundary integral,…
We consider the Liouville theory in fixed Euclidean AdS$_2$ background. Expanded near the minimum of the potential the elementary field has mass squared 2 and (assuming the standard Dirichlet b.c.) corresponds to a dimension 2 operator at…
Based on operator identities and their formal adjoints, we derive two symmetry operators for the linearized Einstein operator on vacuum backgrounds of Petrov type D and in particular the Kerr spacetime. One of them is of differential order…
We study N=1 super Liouville theory on worldsheets with and without boundary. Some basic correlation functions on a sphere or a disc are obtained using the properties of degenerate representations of superconformal algebra. Boundary states…
We investigated the relation between the two-dimensional minimal gravity (Lee-Yang series) with boundaries and open intersection theory. It is noted that the minimal gravity with boundaries is defined in terms of boundary cosmological…
Building on arXiv:1902.03807, this paper develops a unifying study on the boundedness properties of several representative classes of hybrid operators, i.e. operators that enjoy both zero and non-zero curvature features. Specifically, via…
In this article, we consider the minimal $L^2$ integrals related to modules at boundary points on fibrations over open Riemann surfaces, and present a characterization for the concavity property of the minimal $L^2$ integrals degenerating…
We derive a "switching identity" that can be stated for critical Brownian loop-soups or for the Gaussian free field on a cable graph: It basically says that at the level of cluster configurations and at the more general level of the…
Representations of the (Lorentz) conformal group with the soft operators as highest weight vectors have two universal properties, which we clearly state in this paper. Given a soft operator with a certain dimension and spin, the first…
We identify the puncture operator in c=1 Liouville gravity as the discrete state with spin J=1/2. The correlation functions involving this operator satisfy the recursion relation which is characteristic in topological gravity. We derive the…