Distinguished varieties
By Jim Agler, John E. McCarthy. 2005
126 citations recorded by the source corpus.
A distinguished variety is a variety that exits the bidisk through the distinguished boundary. We show that Ando's inequality for commuting matrix contractions can be sharpened to looking at the maximum modulus on a distinguished variety, not the whole bidisk. We show that uniqueness sets for extremal Pick problems on the bidisk always contain a distinguished variety.
Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/988dac40249a64479f034fdfc2194f4d3e21e3e4
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Polynomials defining distinguished varieties (2009, methodology): “If aq̃z + bq̃w has a zero on D2 \ D2, then the left side of (5.1) vanishes to at least order two.”
- A Constrained Nevanlinna-Pick Interpolation Problem (2007, background): “Agler and McCarthy[4] introduced the study of the algebras H∞(V ) of bounded, analytic functions on embedded disks.”
- Spectral sets and distinguished varieties in the symmetrized bidisc (2013, background): “The notion of distinguished variety was introduced by Agler and McCarthy in the bidisc setting in [5].”
- Dilation theory in finite dimensions: the possible, the impossible and the unknown (2010, background): “Every contraction has an N -dilation, so the above theorem is an interesting sharpening of von Neumann’s inequality (for the expert it might be interesting to compare this sharpening with that provided in [1]).”