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On planar Beurling and Fourier transforms

Haakan Hedenmalm
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Abstract

We study the Beurling and Fourier transforms on subspaces of $L^2({\mathbb C})$ defined by an invariance property with respect to the root-of-unity group. This leads to generalizations of these transformations acting unitarily on weighted $L^2$-spaces over $\mathbb C$.

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Haakan Hedenmalm. 2007-01-24. On planar Beurling and Fourier transforms. https://arxiv.org/abs/math/0701696

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