8 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…
Linear Operators on Polynomials and -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, -Positivity Preserver, and their Generators''. The lecture was given at the Universit…
Linear Operators and -Positivity Preserver: A Short Review
Philipp J. di Dio
In the current short review we present the latest developments on linear maps , especially of -positivity preserver, i.e…
Positive Univariate Polynomials: SOS certificates, algorithms, bit complexity, and T-systems
MatÃas Bender, Philipp Di Dio, Elias Tsigaridas
We consider certificates of positivity for univariate polynomials with rational coefficients that are positive over (an interval of)~. Such certificates take the form o…
Characterization of Matrix -Positivity Preserver for and for Compact Sets
Philipp J. di Dio, Lars-Luca Langer
For any closed , in [P.\ J.\ di\,Dio, K.\ Schmüdgen: -Positivity Preserver and their Generators, SIAM J.\ Appl.\ Algebra Geom.\ 9 (2025), 794--824] all…
Absolutely continuous representing measures of complex sequences
Philipp J. di Dio
In 1989, A. J. Duran [Proc. Amer. Math. Soc. 107 (1989), 731-741] showed, that for every complex sequence there exists a Schwartz function $f\in\math…