Klep, Igor; Štrekelj, Tea Facial structure of matrix convex sets. (English) Zbl 1505.46014 J. Funct. Anal. 283, No. 7, Article ID 109601, 55 p. (2022). Reviewer: Ioan Raşa (Cluj-Napoca) MSC: 46A55 46N10 47L07 52A30 PDFBibTeX XMLCite \textit{I. Klep} and \textit{T. Štrekelj}, J. Funct. Anal. 283, No. 7, Article ID 109601, 55 p. (2022; Zbl 1505.46014) Full Text: DOI arXiv
Jury, Michael; Klep, Igor; Mancuso, Mark E.; McCullough, Scott; Pascoe, James Eldred Noncommutative partially convex rational functions. (English) Zbl 1497.46082 Rev. Mat. Iberoam. 38, No. 3, 731-759 (2022). MSC: 46N10 46L89 26B25 47A63 52A41 90C25 PDFBibTeX XMLCite \textit{M. Jury} et al., Rev. Mat. Iberoam. 38, No. 3, 731--759 (2022; Zbl 1497.46082) 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
Jury, Michael; Klep, Igor; Mancuso, Mark E.; McCullough, Scott; Pascoe, James Eldred Noncommutative partial convexity via \(\Gamma\)-convexity. (English) Zbl 1475.46070 J. Geom. Anal. 31, No. 3, 3137-3160 (2021). Reviewer: Stefan Cobzaş (Cluj-Napoca) MSC: 46N10 47L07 52A30 PDFBibTeX XMLCite \textit{M. Jury} et al., J. Geom. Anal. 31, No. 3, 3137--3160 (2021; Zbl 1475.46070) 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
Klep, Igor; Vinnikov, Victor; Volčič, Jurij Local theory of free noncommutative functions: germs, meromorphic functions, and Hermite interpolation. (English) Zbl 1444.32003 Trans. Am. Math. Soc. 373, No. 8, 5587-5625 (2020). MSC: 32A20 47A56 16W60 16R50 32A05 16K40 PDFBibTeX XMLCite \textit{I. Klep} et al., Trans. Am. Math. Soc. 373, No. 8, 5587--5625 (2020; Zbl 1444.32003) 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
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; Klep, Igor; Nelson, Christopher S. Noncommutative polynomials nonnegative on a variety intersect a convex set. (English) Zbl 1327.13090 J. Funct. Anal. 266, No. 12, 6684-6752 (2014). Reviewer: Jose Manuel Gamboa (Madrid) (MR3198852) MSC: 13J30 14A22 46L07 90C22 16S10 14P10 PDFBibTeX XMLCite \textit{J. W. Helton} et al., J. Funct. Anal. 266, No. 12, 6684--6752 (2014; Zbl 1327.13090) Full Text: DOI arXiv
Helton, J. William; Klep, Igor; McCullough, Scott; Slinglend, Nick Noncommutative ball maps. (English) Zbl 1179.47012 J. Funct. Anal. 257, No. 1, 47-87 (2009). Reviewer: Ilie Valuşescu (Bucureşti) MSC: 47A56 46L89 PDFBibTeX XMLCite \textit{J. W. Helton} et al., J. Funct. Anal. 257, No. 1, 47--87 (2009; Zbl 1179.47012) Full Text: DOI arXiv