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.

在处理环上的恒定强度磁性拉普拉斯算子的同时，我们完成了Peetre的工作。特别是，与其不变的光谱相关的本征空间相对于不变的Cauchy-Riemann算子来说是多元分析空间，我们为它们的再生核写下了明确的公式。当磁场强度为整数时，当环的外半径趋于无穷大时，我们将计算获得的核的极限，并通过四阶Jacobi theta函数及其对数导数来表示它们。在相同的量化条件下，我们还推导了它们在环自同构群作用下的变换规则。