On planar Beurling and Fourier transforms

Details On planar Beurling and Fourier transforms On planar Beurling and Fourier transforms

2007-01-24

arxiv.org/abs/math/0701696v1

Ann. Acad. Sci. Fenn. Math. 33 (2008), no. 2, 585--596

Mathematics

Complex Variables

10 pages

Scientific paper

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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