P. D. Dio

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20242026

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cs.CC2025

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)~ $R$ . Such certificates take the form o…

math.FA2025

Characterization of Matrix $K$ -Positivity Preserver for $K = R^{n}$ and for Compact Sets $K \subseteq R^{n}$

Philipp J. di Dio, Lars-Luca Langer

For any closed $K \subseteq R^{n}$ , in [P.\ J.\ di\,Dio, K.\ SchmÃ¼dgen: $K$ -Positivity Preserver and their Generators, SIAM J.\ Appl.\ Algebra Geom.\ 9 (2025), 794--824] all…

math.FA2025

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 $(s_{I^} \pm)_{I^\pm \in N_{0}^{n}}$ there exists a Schwartz function $f\in\math…

Positive Univariate Polynomials: SOS certificates, algorithms, bit complexity, and T-systems

Characterization of Matrix K-Positivity Preserver for K=Rn and for Compact Sets K⊆Rn

Absolutely continuous representing measures of complex sequences

Characterization of Matrix $K$ -Positivity Preserver for $K = R^{n}$ and for Compact Sets $K \subseteq R^{n}$