Watts, Adam Bene; Helton, J. William; Klep, Igor Noncommutative nullstellensätze and perfect games. (English) Zbl 07698494 Ann. Henri Poincaré 24, No. 7, 2183-2239 (2023). MSC: 81Pxx 46Lxx 91Axx PDFBibTeX XMLCite \textit{A. B. Watts} et al., Ann. Henri Poincaré 24, No. 7, 2183--2239 (2023; Zbl 07698494) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij Noncommutative polynomials describing convex sets. (English) Zbl 1471.14120 Found. Comput. Math. 21, No. 2, 575-611 (2021). Reviewer: Tobias Fritz (Innsbruck) MSC: 14P10 15A22 52A05 16W10 16K40 90C22 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Found. Comput. Math. 21, No. 2, 575--611 (2021; Zbl 1471.14120) Full Text: DOI arXiv
Dym, Harry; Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij Plurisubharmonic noncommutative rational functions. (English) Zbl 1460.32071 J. Math. Anal. Appl. 492, No. 1, Article ID 124421, 23 p. (2020). MSC: 32U05 31C10 PDFBibTeX XMLCite \textit{H. Dym} et al., J. Math. Anal. Appl. 492, No. 1, Article ID 124421, 23 p. (2020; Zbl 1460.32071) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott; Volčič, Jurij Bianalytic free maps between spectrahedra and spectraballs. (English) Zbl 1445.47052 J. Funct. Anal. 278, No. 11, Article ID 108472, 61 p. (2020). Reviewer: Mihai Putinar (Santa Barbara) MSC: 47L25 32H02 13J30 14P10 52A05 46L07 PDFBibTeX XMLCite \textit{J. W. Helton} et al., J. Funct. Anal. 278, No. 11, Article ID 108472, 61 p. (2020; Zbl 1445.47052) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott; Schweighofer, Markus Dilations, linear matrix inequalities, the matrix cube problem and beta distributions. (English) Zbl 1447.47009 Memoirs of the American Mathematical Society 1232. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3455-7/pbk; 978-1-4704-4947-6/ebook). vi, 106 p. (2019). Reviewer: Jaydeb Sarkar (Bangalore) MSC: 47-02 47A20 46L07 60E05 33B15 90C22 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Dilations, linear matrix inequalities, the matrix cube problem and beta distributions. Providence, RI: American Mathematical Society (AMS) (2019; Zbl 1447.47009) Full Text: DOI arXiv Backlinks: MO
Evert, Eric; Helton, J. William; Klep, Igor; McCullough, Scott Extreme points of matrix convex sets, free spectrahedra, and dilation theory. (English) Zbl 06902272 J. Geom. Anal. 28, No. 2, 1373-1408 (2018). MSC: 47L07 13J30 46L07 90C22 PDFBibTeX XMLCite \textit{E. Evert} et al., J. Geom. Anal. 28, No. 2, 1373--1408 (2018; Zbl 06902272) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; Volčič, Jurij Geometry of free loci and factorization of noncommutative polynomials. (English) Zbl 1420.16015 Adv. Math. 331, 589-626 (2018). MSC: 16R30 16S36 13J30 14P10 16U30 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Adv. Math. 331, 589--626 (2018; Zbl 1420.16015) Full Text: DOI arXiv
Augat, Meric; Helton, J. William; Klep, Igor; McCullough, Scott Bianalytic maps between free spectrahedra. (English) Zbl 1471.47045 Math. Ann. 371, No. 1-2, 883-959 (2018). MSC: 47L25 14P10 32E30 32H02 46L07 52A05 PDFBibTeX XMLCite \textit{M. Augat} et al., Math. Ann. 371, No. 1--2, 883--959 (2018; Zbl 1471.47045) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott The tracial Hahn-Banach theorem, polar duals, matrix convex sets, and projections of free spectrahedra. (English) Zbl 1457.14123 J. Eur. Math. Soc. (JEMS) 19, No. 6, 1845-1897 (2017). Reviewer: S. S. Kutateladze (Novosibirsk) MSC: 14P10 47L25 90C22 46B25 81P47 15A22 15B48 PDFBibTeX XMLCite \textit{J. W. Helton} et al., J. Eur. Math. Soc. (JEMS) 19, No. 6, 1845--1897 (2017; Zbl 1457.14123) Full Text: DOI arXiv
Evert, Eric; Helton, J. William; Klep, Igor; McCullough, Scott Circular free spectrahedra. (English) Zbl 1351.15011 J. Math. Anal. Appl. 445, No. 1, 1047-1070 (2017). MSC: 15A45 52A05 15A39 PDFBibTeX XMLCite \textit{E. Evert} et al., J. Math. Anal. Appl. 445, No. 1, 1047--1070 (2017; Zbl 1351.15011) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott Matrix convex hulls of free semialgebraic sets. (English) Zbl 1361.46056 Trans. Am. Math. Soc. 368, No. 5, 3105-3139 (2016). Reviewer: Tobias Kaiser (Passau) MSC: 46L89 46L07 14P10 13J30 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Trans. Am. Math. Soc. 368, No. 5, 3105--3139 (2016; Zbl 1361.46056) Full Text: DOI arXiv
Helton, J. William; Nie, Jiawang; Semko, Jeremy S. Free semidefinite representation of matrix power functions. (English) Zbl 1307.90130 Linear Algebra Appl. 465, 347-362 (2015). MSC: 90C22 47H07 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Linear Algebra Appl. 465, 347--362 (2015; Zbl 1307.90130) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott The matricial relaxation of a linear matrix inequality. (English) Zbl 1272.15012 Math. Program. 138, No. 1-2 (A), 401-445 (2013). Reviewer: Mihail Voicu (Iaşi) MSC: 15A39 15A60 14A22 14P10 90C22 11E25 13J30 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Math. Program. 138, No. 1--2 (A), 401--445 (2013; Zbl 1272.15012) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; Mccullough, Scott Convexity and semidefinite programming in dimension-free matrix unknowns. (English) Zbl 1334.90103 Anjos, Miguel F. (ed.) et al., Handbook on semidefinite, conic and polynomial optimization. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). International Series in Operations Research & Management Science 166, 377-405 (2012). MSC: 90C22 90C90 PDFBibTeX XMLCite \textit{J. W. Helton} et al., Int. Ser. Oper. Res. Manag. Sci. 166, 377--405 (2012; Zbl 1334.90103) Full Text: DOI arXiv
Helton, J. William; Nie, Jiawang Semidefinite representation of convex sets and convex hulls. (English) Zbl 1334.90104 Anjos, Miguel F. (ed.) et al., Handbook on semidefinite, conic and polynomial optimization. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). International Series in Operations Research & Management Science 166, 77-112 (2012). MSC: 90C22 90C25 90-02 PDFBibTeX XMLCite \textit{J. W. Helton} and \textit{J. Nie}, Int. Ser. Oper. Res. Manag. Sci. 166, 77--112 (2012; Zbl 1334.90104) Full Text: DOI
Helton, J. William; Nie, Jiawang Semidefinite representation of convex sets. (English) Zbl 1192.90143 Math. Program. 122, No. 1 (A), 21-64 (2010). Reviewer: Do Van Luu (Hanoi) MSC: 90C25 90C22 52A20 46N10 PDFBibTeX XMLCite \textit{J. W. Helton} and \textit{J. Nie}, Math. Program. 122, No. 1 (A), 21--64 (2010; Zbl 1192.90143) Full Text: DOI arXiv