2020/08/31 by Nizar Demni, Zouhaı̈r Mouayn, Zouhair Mouayn
Mathematics · Physics and Astronomy · #Annulus (botany) #Automorphism #Cauchy distribution #Constant function #Invariant (physics) #Laplace operator #Logarithm #Mathematical Analysis and Transform Methods #Mathematical analysis #Mathematical physics #Mathematics #Piecewise #Pure mathematics #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #math-ph #math.CV #math.MP
paper · pdf · doi:10.1088/1751-8121/abcc39
normalising constant is corrected, the Bergman kernel of the punctured disc is retrieved
arxiv created 2020/09/08 · openalex publication_date 2020/11/20 · arxiv updated 2020/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract 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.