Complex Creation Operator and Planar Automorphic Functions

We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This...

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Veröffentlicht in:Mathematical physics, analysis, and geometry analysis, and geometry, 2023-12, Vol.26 (4), Article 28
Hauptverfasser: Allal, Ghanmi, Lahcen, Imlal
Format: Artikel
Sprache:eng
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Zusammenfassung:We provide a concrete characterization of the poly-analytic planar automorphic functions, a special class of non analytic planar automorphic functions with respect to the Appell–Humbert automorphy factor, arising as images of the holomorphic ones by means of the creation differential operator. This is closely connected to the spectral theory of the magnetic Laplacian on the complex plane.
ISSN:1385-0172
1572-9656
DOI:10.1007/s11040-023-09471-8