The quantum theory of a free particle on a portion of two-dimensional Euclidean space bounded by a circle and subject to non-local boundary conditions gives rise to bulk and surface states. Starting from this well known property, a counterpart for gravity is here considered. In particular, if spatial components of metric perturbations are set to zero at the boundary, invariance of the full set ...

in this paper, we study sufficient conditions for existence and uniqueness of solutions of three point boundary vale problem for p-laplacian fractional order differential equations. we use schauder's fixed point theorem for existence of solutions and concavity of the operator for uniqueness of solution. we include some examples to show the applicability of our results.

We consider the linear stationary equation defined by the fractional Laplacian with drift. In the supercritical case, wherein the dominant term is given by the drift instead of the diffusion component, we prove local regularity of solutions in Sobolev spaces employing tools from the theory of pseudo-differential operators. The regularity of solutions in the supercritical case is as expected fro...

We discuss asymptotics of the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold. We obtain an asymptotic formula for the average of the number of states. Furthermore, when the operator has integer eigenvalues and the periodic orbits of period less than 2π of the classical mechanics form clean submanifo...

In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if → : T X X is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximat...

This paper is a further extension of the method proposed in Itkin (2014) as applied to another set of jump-diffusion models: Inverse Normal Gaussian, Hyperbolic and Meixner. To solve the corresponding PIDEs we accomplish few steps. First, a second-order operator splitting on financial processes (diffusion and jumps) is applied to these PIDEs. To solve the diffusion equation we use standard fini...

We consider the elliptic operator P(D)+ V in R , d ≥ 2 where P(D) is a constant coefficient elliptic pseudo-differential operator of order 2 with a homogeneous convex symbol P(ξ), and V is a real periodic function in L∞(Rd). We show that the number of gaps in the spectrum of P(D)+V is finite if 4 > d + 1. If in addition, V is smooth and the convex hypersurface {ξ ∈ R : P(ξ) = 1} has positive Ga...

Let E be a natural operator associated to the curvature tensor of a pseudo-Riemannian manifold. We study when the spectrum, or more generally the real Jordan normal form, of E is constant on the natural domain of definition. In particular, we examine the Jacobi operator, the higher order Jacobi operator, the Szabo operator, and the skew-symmetric curvature operator.