Related papers: Fractional Laplacian in Conformal Geometry
The aim of this paper is to correct a mistake in earlier work on the conformal invariance of Rarita-Schwinger operators and use the method of correction to develop properties of some conformally invariant operators in the Rarita-Schwinger…
This thesis describes a new approach to conformal field theory. This approach combines the method of coadjoint orbits with resolutions and chiral vertex operators to give a construction of the correlation functions of conformal field…
We compute conformally covariant actions and operators for tensors with mixed symmetries in arbitrary dimension $d$. Our results complete the classification of conformal actions that are quadratic on arbitrary tensors with three indices,…
We construct a large family of conformally covariant tridifferential operators as tangential operators in the Fefferman--Graham ambient space. Our construction is analogous to the linear and bilinear constructions of…
Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…
After reviewing the definition of two differential operators which have been recently introduced by Caputo and Fabrizio and, separately, by Atangana and Baleanu, we present an argument for which these two integro-differential operators can…
In this paper we study mixed norm boundedness for fractional integrals related to Laplace--Beltrami operators on compact Riemannian symmetric spaces of rank one. The key point is the analysis of weighted inequalities for fractional integral…
Extended objects such as line or surface operators, interfaces or boundaries play an important role in conformal field theory. Here we propose a systematic approach to the relevant conformal blocks which are argued to coincide with the wave…
We introduce a method of obtaining a higher order extension problem, \'a la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the…
We develop the notion of a (pro-) conformal pseudo operad and apply it to the construction of the basic cohomology complex of a vertex algebra. The paper heavily uses the ideas and constructions of the work of Tamarkin [Tam02]
In this paper we study the obstacle problems for the Navier (spectral) fractional Laplacian $\left(-\Delta_\Omega\right)^{\!s}$ of order $s\in(0,1)$, in a bounded domain $\Omega\subset\mathbb R^n$.
The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we…
Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of…
By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…
In the very influential paper \cite{CS07} Caffarelli and Silvestre studied regularity of $(-\Delta)^s$, $0<s<1$, by identifying fractional powers with a certain Dirichlet-to-Neumann operator. Stinga and Torrea \cite{ST10} and Gal\'e, Miana…
We set up a framework for discussing `$q$-analogues' of the usual covariant differential operators for hermitian symmetric spaces. This turns out to be directly related to the deformation quantization associated to quadratic algebras…
This paper is concerned with the study of a nonlinear problems involving the fractional p(x)-Laplacian operator. By means of the Berkovits degree theory, we prove the existence of nontrivial weak solutions for this problem. The appropriate…
We propose a fractional variant of Mellin's transform which may find an application in the Conformal Field Theory. Its advantage is the presence of an arbitrary parameter which may substantially simplify calculations and help adjusting…
We introduce and study the properties of a new family of fractional differential and integral operators which are based directly on an iteration process and therefore satisfy a semigroup property. We also solve some ODEs in this new model…
We study conformal symmetry breaking differential operators which map differential forms on $\mathbb{R}^n$ to differential forms on a codimension one subspace $\mathbb{R}^{n-1}$. These operators are equivariant with respect to the conformal…