Rational Inner Functions on the Polydisk: A Survey

Greg Knese ()
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Greg Knese: Washington University in St. Louis, Department of Mathematics

Chapter 47 in Operator Theory, 2026, pp 1503-1527 from Springer

Abstract: Abstract 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.

Keywords: Rational inner functions; Blaschke products; Stable polynomials; Rational singularities; von Neumann inequality; Multivariable operator theory; Sums of squares; Interpolation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-032-16356-1_75

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DOI: 10.1007/978-3-032-16356-1_75

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