Sums of even powers of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e20" altimg="si15.svg"><mml:mi>k</mml:mi></mml:math>-regulous functions

Banecki, Juliusz; Kowalczyk, Tomasz

doi:10.1016/j.indag.2022.12.004

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Regulous Valuations 31 the R-valuation Inequality1

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2023

2024

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Cited by 3 publications

(2 citation statements)

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“…It is a result of Hilbert that there exists a homogeneous positive semi-definite polynomial of degree 4 in 4 variables which is not sum of squares of polynomials. By Theorem 3.2 in [1] it is not a sum of squares of 2-regulous functions.…”

Section: Discussionmentioning

confidence: 99%

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Extensions of k-regulous functions from two-dimensional varieties

Banecki¹

2023

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We prove that a k-regulous function defined on a two-dimensional nonsingular affine variety can be extended to an ambient variety. Additionally we derive some results concerning sums of squares of k-regulous functions; in particular we show that every positive semi-definite regular function on a non-singular affine variety can be written as a sum of squares of locally Lipschitz regulous functions.

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Section: Discussionmentioning

confidence: 99%

“…(The notation here is not strictly formal; f (i−1) and f (1) represent some partial derivatives of orders |i| − 1,1 respectively. )…”

Section: Regulous Valuations 31 the R-valuation Inequalitymentioning

confidence: 99%