Publikation:

Natural annihilators and operators of constant rank over C

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2024

Autor:innen

Schiffer, Stefan

Herausgeber:innen

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Deutsche Forschungsgemeinschaft (DFG): 390685813

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Rendiconti Lincei, Matematica e Applicazioni. European Mathematical Society (EMS). 2024, 35(2), S. 155-173. ISSN 1120-6330. eISSN 1720-0768. Verfügbar unter: doi: 10.4171/rlm/1037

Zusammenfassung

Even if the Fourier symbols of two constant rank differential operators have the same nullspace for each non-trivial phase space variable, the nullspaces of those differential operators might differ by an infinite-dimensional space. Under the natural condition of constant rank over C, we establish that the equality of nullspaces on the Fourier symbol level already implies the equality of the nullspaces of the differential operators in D′ modulo polynomials of a fixed degree. In particular, this condition allows one to speak of natural annihilators within the framework of complexes of differential operators.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

Schlagwörter

linear partial differential operators, constant rank operators, elliptic operators, Poincaré lemma

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ISO 690GMEINEDER, Franz, Stefan SCHIFFER, 2024. Natural annihilators and operators of constant rank over C. In: Rendiconti Lincei, Matematica e Applicazioni. European Mathematical Society (EMS). 2024, 35(2), S. 155-173. ISSN 1120-6330. eISSN 1720-0768. Verfügbar unter: doi: 10.4171/rlm/1037
BibTex
@article{Gmeineder2024-11-14Natur-72103,
  title={Natural annihilators and operators of constant rank over C},
  year={2024},
  doi={10.4171/rlm/1037},
  number={2},
  volume={35},
  issn={1120-6330},
  journal={Rendiconti Lincei, Matematica e Applicazioni},
  pages={155--173},
  author={Gmeineder, Franz and Schiffer, Stefan}
}
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