Submitted to the proceedings of the ninth international conference on domain decomposition methods (Bergen-Norway-1996).

We prove a version of Valiron’s conjugacy theorem for Schur class mappings of the unit ball of C . As an application we obtain a formula for the spectral radius of composition operators on the ball with Schur class symbols.

In this paper, using Schur complements, we prove various inequalities in Euclidean Jordan algebras. Specifically, we study analogues of the inequalities of Fischer, Hadamard, Bergstrom, Oppenheim, and other inequalities related to determinants, eigenvalues, and Schur complements.

Over the past years, major attention has been drawn to question of identifying Schur-positive sets, i.e. sets permutations whose associated quasisymmetric function is symmetric and can be written as a non-negative sum Schur functions. The set arc permutations, $\pi$ in $S_n$ such that for any $1\leq j \leq n$, $\{\pi(1),\pi(2),\dots,\pi(j)\}$ an interval $\mathbb{Z}_n$ one most noticeable examp...

The aim of this paper is to give a presentation of several subjects of Schur analysis with some historical information. The class of J-inner functions plays a key role in this new mathematical eld which is situated at the seam of various mathematical disciplines (operator theory, scattering theory, complex function theory, prediction theory for stochastic processes, spectral theory for diierent...

Since the foundation paper of M. Auslander and 0. Goldman [ 1 J, several authors have generalized constructions for studying group algebras over fields to separable algebras over commutative rings. Specifically, we have in mind the Schur index [20], the Schur exponent [18], the Schur group [S], and the uniform group [ 111. This paper gives additional properties of these constructions and studie...

This paper studies the solution of quadratic eigenvalue problems by the quadratic residual iteration method. The focus is on applications arising from nite-element simulations in acoustics. One approach is the shift-invert Arnoldi method applied to the linearized problem. When more than one eigenvalue is wanted, it is advisable to use locking or de-ation of converged eigenvectors (or Schur vect...

The representation theory of Hecke algebras has been an important part toward understanding (ordinary or modular) representation theories of finite groups of Lie type. Schur algebras, as endomorphism algebras, connects the representation theory of general linear groups and the representations of symmetric groups via Schur-Weyl duality. The quantum version of Schur-Weyl duality is established by...