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.

We present an efficient null space free Jacobi-Davidson method to compute the positive eigenvalues of the degenerate elliptic operator arising from Maxwell’s equations. We consider spatial compatible discretizations such as Yee’s scheme which guarantee the existence of a discrete vector potential. During the Jacobi-Davidson iteration, the correction process is applied to the vector potential in...

Suppose L is a lamination of a Riemannian manifold by hypersurfaces with the same constant mean curvature. We prove that every limit leaf of L is stable for the Jacobi operator. A simple but important consequence of this result is that the set of stable leaves of L has the structure of a lamination. Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42

Using the methods of moving frames, we study real hypersurfaces in complex projective space CP and complex hyperbolic space CH whose structure Jacobi operator has various special properties. Our results complement work of several other authors who worked in CPn and CHn for n ≥ 3.

The decay of the parameters {an, bn} for a Jacobi operator J on `(N) is related to the analyticity of the Jost function u(z; J) associated with J , which is in turn related to the spectral measure dμ of J . Damanik and Simon demonstrated the equivalence between the exponential decay of these parameters and the analyticity of the Jost function on a disk whose radius is given by the rate of decay...

Let (Mn,g) be a closed Riemannian manifold and N a warped product manifold of two space forms. We investigate geometric properties by the spectra of the Jacobi operator of a harmonic map φ : M → N . In particular, we show if N is a warped product manifold of Euclidean space with a space form and φ,ψ : M → N are two projectively harmonic maps, then the energy of φ and ψ are equal up to constant ...

We investigate the relationships between the Marcinkiewicz-Zygmund-type inequalities and certain shifted average operators. Applications to the mean boundedness of a quasi-interpolatory operator in the case of trigonometric polynomials, Jacobi polynomials, and Freud polynomials are presented.

Spectral properties of unbounded symmetric Jacobi matrices are studied. Under mild assumptions on the coefficients absolute continuity of spectral measure is proved. Only operator theoretic proofs are provided. Some open problems of Ifantis are solved.