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Articles 1 - 4 of 4
Full-Text Articles in Algebraic Geometry
Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney
Non-Commutative Automorphisms Of Bounded Non-Commutative Domains, John E. Mccarthy, Richard M. Timoney
Mathematics Faculty Research
We establish rigidity (or uniqueness) theorems for non-commutative (NC) automorphisms that are natural extensions of classical results of H. Cartan and are improvements of recent results. We apply our results to NC domains consisting of unit balls of rectangular matrices.
The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy
The Implicit Function Theorem And Free Algebraic Sets, Jim Agler, John E. Mccarthy
Mathematics Faculty Research
We prove an implicit function theorem for non-commutative functions. We use this to show that if p ( X;Y ) is a generic non-commuting polynomial in two variables, and X is a generic matrix, then all solutions Y of p ( X;Y ) = 0 will commute with X
Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy
Aspects Of Non-Commutative Function Theory, Jim Agler, John E. Mccarthy
Mathematics Faculty Research
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
Integrability And Regularity Of Rational Functions, Greg Knese
Integrability And Regularity Of Rational Functions, Greg Knese
Mathematics Faculty Research
Motivated by recent work in the mathematics and engineering literature, we study integrability and non-tangential regularity on the two-torus for rational functions that are holomorphic on the bidisk. One way to study such rational functions is to fix the denominator and look at the ideal of polynomials in the numerator such that the rational function is square integrable. A concrete list of generators is given for this ideal as well as a precise count of the dimension of the subspace of numerators with a specified bound on bidegree. The dimension count is accomplished by constructing a natural pair of commuting …