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Rational inner functions are a generalization of finite Blaschke products to several variables. In this chapter, we survey a variety of results about rational inner functions related to interpolation, sums of squares formulas, and boundary behavior. We mostly focus on two variables; however, in the final section, we discuss higher dimensions.

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Rational Inner Functions on the Polydisk: A Survey

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  • 发表日期：

    2025年

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  • Greg Knese

摘要

Rational inner functions are a generalization of finite Blaschke products to several variables. In this chapter, we survey a variety of results about rational inner functions related to interpolation, sums of squares formulas, and boundary behavior. We mostly focus on two variables; however, in the final section, we discuss higher dimensions.