P. D. Dio

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20242026

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math.AG2026

Making Non-Negative Polynomials into Sums of Squares

Philipp J. di Dio

We study linear operators $T : R [x_{1}, \dots, x_{n}] \to R [x_{1}, \dots, x_{n}]$ , especially for the purpose to move sets $S \subseteq R [x_{1}, \dots, x_{n}]$ into cones $C\sub…

math.FA2026

Linear Operators on Polynomials and $K$ -Positivity Preserver -- A journey from analysis to algebra and back

Philipp J. di Dio

These are the extended lecture notes of my lecture about ``Linear Operators on Polynomials, $K$ -Positivity Preserver, and their Generators''. The lecture was given at the Universit…

math.FA2026

Linear Operators $T : R [x_{1}, \dots, x_{n}] \to R [x_{1}, \dots, x_{n}]$ and $K$ -Positivity Preserver: A Short Review

Philipp J. di Dio

In the current short review we present the latest developments on linear maps $T : R [x_{1}, \dots, x_{n}] \to R [x_{1}, \dots, x_{n}]$ , especially of $K$ -positivity preserver, i.e…

Making Non-Negative Polynomials into Sums of Squares

Linear Operators on Polynomials and K-Positivity Preserver -- A journey from analysis to algebra and back

Linear Operators T:R[x1​,…,xn​]→R[x1​,…,xn​] and K-Positivity Preserver: A Short Review

Linear Operators on Polynomials and $K$ -Positivity Preserver -- A journey from analysis to algebra and back

Linear Operators $T : R [x_{1}, \dots, x_{n}] \to R [x_{1}, \dots, x_{n}]$ and $K$ -Positivity Preserver: A Short Review