Algebraic properties of Hermitian sums of squares

被引：3
|
作者：
Brooks, Jennifer [1 ,3 ]
Grundmeier, Dusty [2 ]
机构：
[1] Univ Montana, Dept Math Sci, Missoula, MT 59812 USA
[2] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[3] Brigham Young Univ, Dept Math, Provo, UT 84602 USA
来源：
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2020年 / 65卷 / 04期
关键词：
H; Boas; Sums of squares; real polynomials; Betti numbers; POSITIVITY;
D O I：
10.1080/17476933.2019.1652276
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the class of bihomogeneous polynomials on for which there is a positive integer d such that can be written as a Hermitian sum of squares. We reinterpret this problem in terms of commutative algebra, and we give necessary algebraic conditions on this class of polynomials.
引用
收藏
页码：695 / 712
页数：18
相关论文
共 50 条
  • [1] ALGEBRAIC PROPERTIES OF HERMITIAN SUMS OF SQUARES, II
    Brooks, Jennifer
    Grundmeier, Dusty
    Schenck, Hal
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 150 (08) : 3471 - 3476
  • [2] SUMS OF HERMITIAN SQUARES
    LEWIS, DW
    JOURNAL OF ALGEBRA, 1988, 115 (02) : 466 - 480
  • [3] Spectral properties of sums of Hermitian matrices and algebraic geometry
    Huu-Tai, P. Chau
    Van Isacker, P.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (15)
  • [4] Sums of Hermitian Squares and the BMV Conjecture
    Klep, Igor
    Schweighofer, Markus
    JOURNAL OF STATISTICAL PHYSICS, 2008, 133 (04) : 739 - 760
  • [5] SUMS OF HERMITIAN SQUARES ON PSEUDOCONVEX BOUNDARIES
    Putinar, Mihai
    Scheiderer, Claus
    MATHEMATICAL RESEARCH LETTERS, 2010, 17 (06) : 1047 - 1053
  • [6] Sums of Hermitian Squares and the BMV Conjecture
    Igor Klep
    Markus Schweighofer
    Journal of Statistical Physics, 2008, 133 : 739 - 760
  • [7] Sums of Hermitian squares as an approach to the BMV conjecture
    Burgdorf, Sabine
    LINEAR & MULTILINEAR ALGEBRA, 2011, 59 (01): : 1 - 9
  • [8] Matrix Completions, Moments, and Sums of Hermitian Squares
    Kerchy, Laszlo
    ACTA SCIENTIARUM MATHEMATICARUM, 2011, 77 (3-4): : 725 - 725
  • [9] Connes' embedding conjecture and sums of hermitian squares
    Klep, Igor
    Schweighofer, Markus
    ADVANCES IN MATHEMATICS, 2008, 217 (04) : 1816 - 1837
  • [10] Sums of squares on real algebraic surfaces
    Claus Scheiderer
    manuscripta mathematica, 2006, 119 : 395 - 410
12345