Polyanalytic reproducing Kernels on the quantized annulus

While dealing with the constant-strength magnetic Laplacian on the annulus, we complete Peetre's work. In particular, the eigenspaces associated with its discrete spectrum true turns out to be polyanalytic spaces with respect to the invariant Cauchy-Riemann operator, and we write down explicit...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2021-01, Vol.54 (1), p.15209
Main Authors: Demni, Nizar, Mouayn, Zouhair
Format: Article
Language:English
Subjects:
fourth Jacobi theta function
invariant Cauchy-Riemann operator
magnetic laplacian
Mathematical Physics
Mathematics
polyanalytic spaces
Quantized annulus
reproducing kernels
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Summary:While dealing with the constant-strength magnetic Laplacian on the annulus, we complete Peetre's work. In particular, the eigenspaces associated with its discrete spectrum true turns out to be polyanalytic spaces with respect to the invariant Cauchy-Riemann operator, and we write down explicit formulas for their reproducing kernels. When the magnetic field strength is an integer, we compute the limits of the obtained kernels when the outer radius of the annulus tends to infinity and express them by means of the fourth Jacobi theta function and of its logarithmic derivatives. Under the same quantization condition, we also derive their transformation rule under the action of the automorphism group of the annulus.
ISSN:1751-8113
1751-8121
DOI:10.1088/1751-8121/abcc39