Philipp J. di Dio

collaborators

4 papers

math.FA2024

Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities

Philipp J. di Dio

In this work we investigate and characterize linear functionals $L : R [x_{1}, \dots, x_{n}] \to R$ with absolutely continuous representing measures $μ$ , i.e., $\mathrm{d}μ(…

math.FA2024

$K$ -Positivity Preservers and their Generators

Philipp J. di Dio, Konrad Schmüdgen

We study $K$ -positivity preservers with given closed $K \subseteq R^{n}$ , i.e., linear maps $T : R [x_{1}, \dots, x_{n}] \to R [x_{1}, \dots, x_{n}]$ such that $T\mathrm{Pos}(…

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…

Absolutely Continuous Representing Measures of Moment Sequences with an Emphasis on the Regularity of the Densities

K-Positivity Preservers and their Generators

An Introduction to T-Systems -- with a special Emphasis on Sparse Moment Problems, Sparse Positivstellensätze, and Sparse Nichtnegativstellensätze

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

$K$ -Positivity Preservers and their Generators