30 citations · 48 across the 11 of their papers we have counts for
11 papers
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…
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,…
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…
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…
On Positivity Preservers with constant Coefficients and their Generators
Philipp J. di Dio
In this work we study positivity preservers with constant coefficients and define their generators if they exist, i.e.…
Time-dependent moments from partial differential equations and the time-dependent set of atoms
Raúl E. Curto, Philipp J. di Dio, Milan Korda +1
We study the time-dependent moments and associated polynomials arising from the partial differential equation , and consider in deta…
Time-dependent moments from the heat equation and a transport equation
Raul E. Curto, Philipp di Dio
We present a new connection between the classical theory of full and truncated moment problems and the theory of partial differential equations, as follows. For the classical heat…
Schwartz Function Valued Solutions of the Euler and the Navier-Stokes Equations
Philipp J. di Dio
We prove the existence of a solution for the second order system of partial differential equations by a Montel space versi…
The multidimensional truncated Moment Problem: Carathéodory Numbers from Hilbert Functions
Philipp J. di Dio, Mario Kummer
In this paper we improve the bounds for the Carathéodory number, especially on algebraic varieties and with small gaps (not all monomials are present). We provide explicit lower an…
The multidimensional truncated Moment Problem: Carathéodory Numbers
Philipp J. di Dio, Konrad Schmüdgen
Let be a finite-dimensional subspace of , where is a locally compact Hausdorff space, and a ba…
The multidimensional truncated Moment Problem: Atoms, Determinacy, and Core Variety
Philipp J. di Dio, Konrad Schmüdgen
This paper is about the moment problem on a finite-dimensional vector space of continuous functions. We investigate the structure of the convex cone of moment functionals (supporti…