Related papers: On fractional GJMS operators
We discuss conformally covariant differential operators, which under local rescalings of the metric, \delta_\sigma g^{\mu\nu} = 2 \sigma g^{\mu\nu}, transform according to \delta_\sigma \Delta = r \Delta \sigma + (s-r) \sigma \Delta for…
On locally conformally flat manifolds we describe a construction which maps generalised conformal Killing tensors to differential operators which may act on any conformally weighted tensor bundle; the operators in the range have the…
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…
The Weak Gravity Conjecture is typically stated as a bound on the mass-to-charge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is…
We show that a Krein-Feller operator is naturally associated to a fixed measure $\mu$, assumed positive, $\sigma$-finite, and non-atomic. Dual pairs of operators are introduced, carried by the two Hilbert spaces, $L^{2}\left(\mu\right)$ and…
In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…
The concept of electric-magnetic duality can be extended to linearized gravity. It has indeed been established that in four dimensions, the Pauli-Fierz action (quadratic part of the Einstein-Hilbert action) can be cast in a form that is…
For even dimensional conformal manifolds several new conformally invariant objects were found recently: invariant differential complexes related to, but distinct from, the de Rham complex (these are elliptic in the case of Riemannian…
In this paper, we first define a discrete version of the fractional Laplace operator $(-\Delta)^{s}$ through the heat semigroup on a stochastically complete, connected, locally finite graph $G = (V, E, \mu, w)$. Secondly, we define the…
We extend and clarify the large-charge expansion of the conformal dimension $\Delta_Q$ of the lowest operator of charge $Q$ in nonrelativistic CFTs using the state-operator correspondence. The latter requires coupling the theory to an…
We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas of the time frequency analysis, we show that such operators are uniformly…
By means of a new mod(N)-invariant operator basis, s-parametrized phase-space functions associated with bounded operators in a finite-dimensional Hilbert space are introduced in the context of the extended Cahill-Glauber formalism, and…
Motivated by AdS/CFT, the extension is made to spin-half of a scalar calculation of the conformal anomalies and functional determinants of GJMS operators. The formal aspects are heuristic but sufficient. A Barnes zeta function…
Let $\Omega \subset {\bf R}^d$ be an open bounded set with Lipschitz boundary $\Gamma$. Let $D_V$ be the Dirichlet-to-Neumann operator with respect to a purely second-order symmetric divergence form operator with real Lipschitz continuous…
We introduce three one-parameter semigroups of operators and determine their spectra. Two of them are fractional integrals associated with the Askey-Wilson operator. We also study these families as families of positive linear approximation…
The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…
In this paper we introduce conformally covariant boundary operators for Poincar\'e-Einstein manifolds satisfying a mild spectral assumption. Using these boundary operators we set up higher order Dirichlet problems whose solutions are such…
We establish that the spectral multiplier $\frak{M}(G_{\alpha})$ associated to the differential operator $$ G_{\alpha}=- \Delta_x +\sum_{j=1}^m{{\alpha_j^2-1/4}\over{x_j^2}}-|x|^2 \Delta_y \; \text{on} (0,\infty)^m \times \R^n,$$ which we…
We go beyond a systematic review of the semiclassical approaches for determining the scaling dimensions of fixed-charge operators in $U(1)$ and $O(N)$ models by introducing a general strategy apt at determining the relation between a given…
This discussion paper presents some parts of the work in progress. It is shown that G.W. Leibniz was the first who raised the question about geometric interpretation of fractional-order operators. Geometric interpretations of the…