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Article Dans Une Revue Journal of Physics A: Mathematical and Theoretical Année : 2021

Polyanalytic reproducing Kernels on the quantized annulus

Nizar Demni
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Zouhair Mouayn
  • Fonction : Auteur

Résumé

While dealing with the constant-strength magnetic Laplacian on the annulus, we complete J. Peetre's work. In particular, the eigenspaces associated with its discrete spectrum are true-polyanalytic spaces with respect to the invariant Cauchy-Riemann operator, and we write down explicit formulas for their reproducing kernels. The latter are expressed by means of the fourth Jacobi theta function and of its logarithmic derivatives when the magnetic field strength is an integer. Under this quantization condition, we also derive the transformation rule satisfied by the reproducing kernel under the automorphism group of the annulus.

Dates et versions

hal-03170458 , version 1 (16-03-2021)

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Citer

Nizar Demni, Zouhair Mouayn. Polyanalytic reproducing Kernels on the quantized annulus. Journal of Physics A: Mathematical and Theoretical, 2021, 54 (1), pp.015209. ⟨10.1088/1751-8121/abcc39⟩. ⟨hal-03170458⟩
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