We present an abstract convergence result for the fixed point approximation of stationary Hamilton–Jacobi equations. The basic assumptions on the discrete operator are invariance with respect to the addition of constants, ε-monotonicity and consistency. The result can be applied to various high-order approximation schemes which are illustrated in the paper. Several applications to Hamilton–Jaco...

Abstract We study the Li–Yau inequality for heat equation corresponding to Dunkl harmonic oscillator, which is a nonlocal Schrödinger operator parameterized by reflections and multiplicity functions. In particular case when reflection group isomorphic ℤ 2 d {\mathbb{Z}...

We study the higher order Jacobi operator in pseudo-Riemannian geometry. We exhibit a family of manifolds so that this operator has constant Jordan normal form on the Grassmannian of subspaces of signature (r, s) for certain values of (r, s). These pseudo-Riemannian manifolds are new and nontrivial examples of higher order Osserman manifolds. Subject Classification: 53B20. PACS numbers: 0240, 0...

In this paper, we introduce a new notion of quadratic Killing normal Jacobi operator (simply, operator) and its geometric meaning for real hypersurfaces in the complex Grassmannians rank two G2m+2(c), c≠0. addition, give classification theorems Hopf with two-plane compact type non-compact type.

In this paper, we establish real Paley-Wiener theorems for the Dunkl transform on IR d. More precisely, we characterize the functions in the Schwartz space S(IR d) and in L 2 k (IR d) whose Dunkl transform has bounded, unbounded, convex and nonconvex support. 1 Introduction In the last few years there has been a great interest to real Paley-Wiener theorems for certain integral transforms, see [...

The Dunkl transform is an integral transform on R" which generalises the classical Fourier transform. On suitable function spaces, it establishes a natural correspondence between the action of multiplication operators on one hand and so-called Dunkl operators on the other. These are differential-difference operators, generalising the usual partial derivatives, which are associated with a finite...