Norm preserving extensions of holomorphic functions from subvarieties of the bidisk

By Jim Agler, John E. McCarthy. 2004

64 citations recorded by the source corpus.

A basic result in the theory of holomorphic functions of several complex variables is the following special case of the work of H. Cartan on the sheaf cohomology on Stein domains ([10], or see [14] or [16] for more modern treatments).

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f4b11195944267d7c9ba7cebe6d3c9cb727cdb2f

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In Applied Mathematics

1. Jim Agler
2. John E. McCarthy
3. Joseph A. Ball
4. Victor Vinnikov
5. Gregory Marx
6. Orr Shalit
7. Greg Knese
8. N. Young

In Geometry and Topology

1. Jim Agler
2. John E. McCarthy

Citations in the corpus

• Distinguished varieties (2005, background): “The extension problem (b) is non-trivial: unless the distinguished variety is isomorphic to a disk, there will always be some functions that cannot be extended to the whole bidisk without increasing the norm [5].”
• Pick Interpolation for free holomorphic functions (2013, background): “Unless V ∩D2 is a retract of D2, one can by [1] always find some p0 so that (6.”