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NONNEGATIVE POLYNOMIALS, SUMS OF SQUARES AND THE MOMENT PROBLEM

Part of: Basic linear algebra General theory of linear operators Topological rings and modules Integral transforms, operational calculus Forms and linear algebraic groups Selfadjoint operator algebras

Published online by Cambridge University Press:  19 February 2021

ABHISHEK BHARDWAJ Open the ORCID record for ABHISHEK BHARDWAJ [Opens in a new window]
ABHISHEK BHARDWAJ*
Affiliation:
Laboratoire d’analyse et d’architecture des systèmes (LAAS), Centre National de la Recherche Scientifique, 31400Toulouse, France
*
e-mail: [email protected]
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Abstract

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Keywords

completely positive mapsmoment problemmomentspolynomial optimisationpositive mapsquantum informationsums of squares

MSC classification

Primary: 11E25: Sums of squares and representations by other particular quadratic forms
Secondary: 13J30: Real algebra 15A45: Miscellaneous inequalities involving matrices 44A60: Moment problems 46L07: Operator spaces and completely bounded maps 47A57: Operator methods in interpolation, moment and extension problems 81P45: Quantum information, communication, networks 90C22: Semidefinite programming
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 337 - 341
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the Australian National University in February 2020; degree approved on 27 July 2020; supervisors Martin Helmer and Igor Klep.

References

Bhardwaj, A., Trace Positive, Non-commutative Polynomials and the Truncated Moment Problem, Master’s Thesis, University of Auckland, 2016, https://researchspace.auckland.ac.nz.Google Scholar
Bhardwaj, A., Non-negative Polynomials, Sums of Squares & the Moment Problem, PhD Thesis, The Australian National University, Canberra, 2020, http://openresearch-repository.anu.edu.au.CrossRefGoogle Scholar
Bhardwaj, A. and Zalar, A., ‘The singular bivariate tracial moment problem’, Complex Anal. Oper. Theory 12 (2018), 1057–1142.CrossRefGoogle Scholar
Blekherman, G., Smith, G. and Velasco, M., ‘Sums of squares and varieties of minimal degree’, J. Amer. Math. Soc. 29(3) (2016), 893–913.CrossRefGoogle Scholar
Burgdorf, S. and Klep, I., ‘Trace-positive polynomials and the quartic tracial moment problem’, C. R. Math. 348(13–14) (2010), 721–726.CrossRefGoogle Scholar
Klep, I., McCullough, S., Šivic, K. and Zalar, A., ‘There are many more positive maps than completely positive maps’, Int. Math. Res. Not. 2019(11) (2019), 3313–3375.CrossRefGoogle Scholar