Sharp Schwarz-type Lemmas for the Spectral Unit Ball

An extension theorem for finite positive measures on surfaces of finite‎ ‎dimensional unit balls in Hilbert spaces

A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kante...

Some New Observations on Interpolation in the Spectral Unit Ball

We present several results associated to a holomorphic-interpolation problem for the spectral unit ball Ωn, n ≥ 2. We begin by showing that a known necessary condition for the existence of a O(D; Ωn)-interpolant (D here being the unit disc in C), given that the matricial data are non-derogatory, is not sufficient. We provide next a new necessary condition for the solvability of the two-point in...

Schwarz-type lemmas for solutions of ¯∂-inequalities and complete hyperbolicity of almost complex manifolds.

Sharp Bounds on the PI Spectral Radius

In this paper some upper and lower bounds for the greatest eigenvalues of the PI and vertex PI matrices of a graph G are obtained. Those graphs for which these bounds are best possible are characterized.

On Non-overlapping Domain Decomposition Preconditioners for Discontinuous Galerkin Finite Element Methods in H-type Norms

Abstract. We analyse the spectral bounds of non-overlapping domain decomposition additive Schwarz preconditioners for hp-version discontinuous Galerkin finite element methods in H-type norms. Using original approximation results for discontinuous finite element spaces, it is found that these preconditioners yield a condition number bound of order 1 + Hp/hq, where H and h are respectively the co...