John E. McCarthy

activity

19962026

most citedThe Smirnov class for spaces with the complete Pick property

38 citations · 253 across the 49 of their papers we have counts for

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3 papers · 1 filter

math.AG2014★ 1 cited

The implicit function theorem and free algebraic sets

Jim Agler, John E. McCarthy

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 gener…

math.AG2007

Cusp Algebras

Jim Agler, John E. McCarthy

We consider simple cusp algebras, that is certain subalgebras of the algebra of holomorphic functions on a disk that are annihilated by some distributions living on a singleton. We…

math.AG2005

Toral Algebraic Sets and Function Theory on Polydisks

Jim Agler, John McCarthy, Mark Stankus

A toral algebraic set $A$ is an algebraic set in $\C^n$ whose intersection with $\T^n$ is sufficiently large to determine the holomorphic functions on $A$ . We develop the theory of…