4 papers
math.AG2025
Making Non-Negative Polynomials into Sums of Squares
Philipp J. di Dio
We study linear operators , especially for the purpose to move sets into cones $C\sub…
math.FA2024
The Hadamard Product of Moment Sequences, Diagonal Positivity Preservers, and their Generators
Philipp J. di Dio, Lars-Luca Langer
In this work we investigate special aspects of positivity preservers and especially diagonal positivity preservers, i.e., linear maps $T:\mathbb{R}[x_1,\dots,x_n]\to\mathbb{R}[x_1,…
math.CA2024
An Introduction to T-Systems -- with a special Emphasis on Sparse Moment Problems, Sparse Positivstellensätze, and Sparse Nichtnegativstellensätze
Philipp J. di Dio
These are the lecture notes based on [dD23] for the (upcoming) lecture "T-systems with a special emphasis on sparse moment problems and sparse Positivstellensätze" in the summer se…
math.CA2023
The Early History of Moment Problems and Non-Negative Polynomials with Gaps: Sparse Moment Problems, Sparse Positivstellensätze, and Sparse Nichtnegativstellensätze from a T-System Point of View
Philipp J. di Dio
We deal with and investigate sparse univariate Positivstellensätze, Nichtnegativstellensätze, and solutions to sparse moment problems. The paper relies heavily on results on T-syst…