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Algebraic properties of Hermitian sums of squares, II.
- Source :
-
Proceedings of the American Mathematical Society . Aug2022, Vol. 150 Issue 8, p3471-3476. 6p. - Publication Year :
- 2022
-
Abstract
- We study real bihomogeneous polynomials r(z,\bar {z}) in n complex variables for which r(z,\bar {z}) \left \lVert {z} \right \rVert ^2 is the squared norm of a holomorphic polynomial mapping. Such polynomials are the focus of the Sum of Squares Conjecture, which describes the possible ranks for the squared norm r(z,\bar {z}) \left \lVert {z} \right \rVert ^2 and has important implications for the study of proper holomorphic mappings between balls in complex Euclidean spaces of different dimension. Questions about the possible signatures for r(z,\bar {z}) and the rank of r(z,\bar {z}) \left \lVert {z} \right \rVert ^2 can be reformulated as questions about polynomial ideals. We take this approach and apply purely algebraic tools to obtain constraints on the signature of r. [ABSTRACT FROM AUTHOR]
- Subjects :
- *SUM of squares
*HOLOMORPHIC functions
*COMPLEX variables
*POLYNOMIALS
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 150
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 157430892
- Full Text :
- https://doi.org/10.1090/proc/15900