Noncommutative plurisubharmonic polynomials part I: Global assumptions

Plurisubharmonic Polynomials and Bumping

We wish to study the problem of bumping outwards a pseudoconvex, finite-type domain Ω ⊂ C in such a way that pseudoconvexity is preserved and such that the lowest possible orders of contact of the bumped domain with ∂Ω, at the site of the bumping, are explicitly realised. Generally, when Ω ⊂ C, n ≥ 3, the known methods lead to bumpings with high orders of contact — which are not explicitly know...

A local-global principle for linear dependence of noncommutative polynomials

A set of polynomials in noncommuting variables is called locally linearly dependent if their evaluations at tuples of matrices are always linearly dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally linearly dependent set of polynomials is linearly dependent. In this short note an alternative proof based on the theory of polynomial identities is given. The method of the ...

.................. PART ONE: SYMMETRY.................. I. Global

The iteration of cubic polynomials Part I: The global topology of parameter space

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 CHAPTER I. Univalent functions in complex analytic dynamics . . . . . . 147 1. Attraction to infinity . . . . . . . . . . . . . . . . . . . . . . . 147 2. Parametrizing the space of polynomials . . . . . . . . . . . . . 150 3. Compactness of the connectedness locus . . . . . . . . . . . . 153 4. The mapping q~e is ...

Noncommutative Symmetric Hall-Littlewood Polynomials

Noncommutative symmetric functions have many properties analogous to those of classical (commutative) symmetric functions. For instance, ribbon Schur functions (analogs of the classical Schur basis) expand positively in noncommutative monomial basis. More of the classical properties extend to noncommutative setting as I will demonstrate introducing a new family of noncommutative symmetric funct...