Every convex free basic semi-algebraic set has an LMI representation

By J. William Helton, Scott McCullough. 2012

105 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Electrical and Electronic Engineering, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8d8bc852cd1c540cad081829f1c43b3fb7b83f65

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

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

In Electrical and Electronic Engineering

1. John E. McCarthy
2. Victor Vinnikov
3. Jim Agler

In Geometry and Topology

1. Jim Agler
2. John E. McCarthy
3. Victor Vinnikov
4. Gregory Marx
5. Joseph A. Ball

Citations in the corpus

• Global Holomorphic Functions in Several Noncommuting Variables (2015, unknown): “of bounded operators; Ball, Groenewald and Malakorn [10], in the context of extending realization formulas from functions of commuting operators to functions of non-commuting operators; Alpay and Kalyuzhnyi-Verbovetzkii [6] in the context of realization formulas for rational functions that are J-uni”
• Noncommutative reproducing kernel Hilbert spaces (2016, background): “ependently in the work of Voiculescu and collaborators (see [49, 50]) in the context of the needs of a free-probability theory, as well as in the work of Helton-Klep-McCullough and collaborators (see [25, 26, 27, 29, 11]) on free noncommutative Linear-Matrix-Inequality relaxations and connections wi”
• Pick Interpolation for free holomorphic functions (2013, background): “In [14], Bergman, Helton and McCullough proved that IV is the smallest ideal containing A, provided this ideal is finitely generated.”
• LMI Representations of Convex Semialgebraic Sets and Determinantal Representations of Algebraic Hypersurfaces: Past, Present, and Future (2012, methodology): “t one of the several important problems of this kind arising from SDP. Other major problems have to do with lifted LMI representations (see [35, 25, 26]) and with the free noncommutative setting (see [24, 23]). DETERMINANTAL REPRESENTATIONS: PAST, PRESENT, AND FUTURE 3 Acknowledgments. Apart from my”
• Interpolation and transfer-function realization for the noncommutative Schur-Agler class (2016, background): “Closely related approaches to and results on such a “free noncommutative function theory” can be found in the work of Voiculescu [81, 82] and Helton-Klep-McCullough [45, 46, 47].”