Hilbert's Nullstellensatz for analytic trigonometric polynomials

DOI10.1016/j.exmath.2022.09.005zbMath1505.12001OpenAlexW4307995547MaRDI QIDQ2105647

Jie Xiao, Cheng Yuan

Publication date: 8 December 2022

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2022.09.005

zbMATH Keywords

complex planeHilbert's NullstellensatzPythagoras' identity

Mathematics Subject Classification ID

Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Entire functions of one complex variable (general theory) (30D20) (overlinepartial) and (overlinepartial)-Neumann operators (32W05)

Cites Work

• Fields of large transcendence degree generated by values of elliptic functions
• Bounds for the degrees in the Nullstellensatz
• \(\bar{\partial}\)-equation look at analytic Hilbert's zero-locus theorem
• Cauchy-Riemann \(\bar{\partial}\)-equations with some applications
• Projection factors and generalized real and complex Pythagorean theorems
• Interpolations by bounded analytic functions and the corona problem
• An analytic approach to the degree bound in the Nullstellensatz
• Sharp Effective Nullstellensatz

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