# On the Bergman projection and kernel in periodic planar domains

@inproceedings{Taskinen2021OnTB, title={On the Bergman projection and kernel in periodic planar domains}, author={Jari Taskinen}, year={2021} }

We study Bergman kernels KΠ and projections PΠ in unbounded planar domains Π, which are periodic in one dimension. In the case Π is simply connected we write the kernel KΠ in terms of a Riemann mapping φ related to the bounded periodic cell ̟ of the domain Π. We also introduce and adapt to the Bergman space setting the Floquet transform technique, which is a standard tool for elliptic spectral problems in periodic domains. We investigate the boundedness properties of the Floquet transform… Expand

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