## Singular values and Schmidt pairs of composition operators on the Hardy space.(English)Zbl 1066.47026

The main result of the present paper solves the functional equation $G(z)f(\varphi(z))=\lambda f(z),$ where $$G$$ is a given bounded analytic function in the unit disk $$D$$ and $$\varphi$$ is a given analytic self-map of $$D$$. The unknowns of the equation are $$f$$, which is to be analytic in $$D$$, and $$\lambda$$, which is to be a complex number. As a consequence, the singular values of the compact composition operator $$C_\varphi$$ on the classical Hardy space $$H^2$$ are computed, where $$\varphi(z)=az+b$$ with $$| a| +| b| <1$$. The corresponding problem for weighted Bergman spaces is discussed as well.
Reviewer: Kehe Zhu (Albany)

### MSC:

 47B33 Linear composition operators 30H05 Spaces of bounded analytic functions of one complex variable 39B32 Functional equations for complex functions
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### References:

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