On positivity preservers with constant coefficients and their generators

di Dio, Philipp J.

On positivity preservers with constant coefficients and their generators

Dateien

diDio_2-k3ku045wig5h3.pdfGröße: 520.77 KBDownloads: 8

Datum

2024

Angaben zur Forschungsförderung

Deutsche Forschungsgemeinschaft (DFG): DI-2780/2-1

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik
Zukunftskolleg

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Journal of Algebra. Elsevier. 2024, 660, S. 882-907. ISSN 0021-8693. eISSN 1090-266X. Verfügbar unter: doi: 10.1016/j.jalgebra.2024.07.050

Zusammenfassung

In this work we study positivity preservers T : R[x₁, ..., xn] → R[x1, ..., x_n] with constant coefficients and define their generators A if they exist, i.e., exp(A) = T. We use the theory of regular Fréchet Lie groups to show the first main result. A positivity preserver with constant coefficients has a generator if and only if it is represented by an infinitely divisible measure (Main Theorem 4.7). In the second main result (Main Theorem 4.11) we use the Lévy–Khinchin formula to fully characterize the generators of positivity preservers with constant coefficients.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Positivity preserver, Generator, Constant coefficient, Moments

Zitieren

ISO 690

DI DIO, Philipp J., 2024. On positivity preservers with constant coefficients and their generators. In: Journal of Algebra. Elsevier. 2024, 660, S. 882-907. ISSN 0021-8693. eISSN 1090-266X. Verfügbar unter: doi: 10.1016/j.jalgebra.2024.07.050

BibTex

@article{diDio2024-12posit-70655,
  year={2024},
  doi={10.1016/j.jalgebra.2024.07.050},
  title={On positivity preservers with constant coefficients and their generators},
  volume={660},
  issn={0021-8693},
  journal={Journal of Algebra},
  pages={882--907},
  author={di Dio, Philipp J.}
}

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