Pick Interpolation for free holomorphic functions
By Jim Agler, John E. McCarthy. 2013
66 citations recorded by the source corpus.
We give necessary and sufficient conditions to solve an interpolation problem for free holomorphic functions bounded in norm on a free polynomial polyhedron. As an application, we prove that every bounded holomorphic function on a polynomial polyhedron extends to a bounded free function.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/9f6cfb115279b88344722e241fcad0d6d55d273a
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In Applied Mathematics
- Victor Vinnikov
- Orr Shalit
- Joseph A. Ball
- Gregory Marx
- Guy Salomon
- E. Shamovich
- Jim Agler
- John E. McCarthy
Citations in the corpus
- Interpolation and transfer-function realization for the noncommutative Schur-Agler class (2016, methodology): “A new feature for the noncommutative setting of Theorem 3.1, first observed by Agler-McCarthy in [7], is that the cone separation argument still applies with a localized weaker version (see condition (1′) in Theorem 3.1) of condition (1) as a hypothesis.”
- Global Holomorphic Functions in Several Noncommuting Variables (2015, methodology): “We need the following theorem from [3]:”
- Algebras of bounded noncommutative analytic functions on subvarieties of the noncommutative unit ball (2017, result): “Moreover, Agler and McCarthy proved in [1] that this space is universal among the spaces with the complete Pick property.”
- Noncommutative reproducing kernel Hilbert spaces (2016, methodology): “heory of minimal decompositions and Brangesian complementary spaces. In our followup paper [13] we use various parts of the material in the present paper to develop further the work of Agler-McCarthy [2, 3] on noncommutative Pick interpolation and transfer-function realization and introduce a free n”
- The implicit function theorem and free algebraic sets (2014, unknown): “…the free topology there is an Oka-Weil theorem, and in particular every free holomorphic function f has the property that f ( x ) is in the algebra generated by x for every x in the domain [1]; this property was crucial in the authors’ study of Pick interpolation for free holomorphic functions [2].”