论文标题
量化环上的多芯片再现核
Polyanalytic Reproducing Kernels on the Quantized Annulus
论文作者
论文摘要
在与环上的恒定强度磁拉曲板打交道时，我们完成了J. Peetre的工作。特别是，与其离散谱相关的特征空间相对于不变的cauchy-riemann运算符是真正的流分析空间，我们为其再现核写下了明确的公式。当磁场强度是整数时，后者是通过第四个雅各比theta函数及其对数衍生物表示的。在这种量化条件下，我们还得出了通过环形群体下的复制内核满足的转换规则。
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.
