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Commutant lifting, interpolation, and perturbations on the polydisc

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arxiv 2301.10020 v3 pith:WHNZZAXN submitted 2023-01-24 math.FA math.CVmath.OA

Deepak K. D. , Jaydeb Sarkar This is my paper · ORCID
classification math.FAmath.CVmath.OA
keywords liftingcommutantpolydiscinterpolationproblemsolveanalyticbounded
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The fundamental theorem on commutant lifting due to Sarason does not carry over to the setting of the polydisc. This paper presents two classifications of commutant lifting in several variables. The first classification links the lifting problem to the contractivity of certain linear functionals. The second one transforms it into nonnegative real numbers via a distance formula. We also solve the Nevanlinna-Pick interpolation problem for bounded analytic functions on the polydisc. Along the way, we solve a perturbation problem for bounded analytic functions. Commutant lifting and interpolation on the polydisc solve two well-known problems in Hilbert function space theory.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Dynamical Frames and Hyperinvariant Subspaces

    math.FA 2025-05 accept novelty 7.0 of 10

    Every frame representation of Z_+^k is central: any two frames built from the joint orbits of a commuting k-tuple are linked by an invertible operator commuting with all the operators.

  2. Function theory of the hexablock and applications to the tetrablock and Euclidean biball

    math.CV 2026-08 conditional novelty 6.0 of 10

    The paper proves realization, interpolation, extension, and Toeplitz corona theorems for the hexablock, recovering the tetrablock and biball results as special cases.

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