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Analytic Interpolation into the Tetrablock and a μ-synthesis Problem

  • Zinaida A. Lykova
  • N. J. Young
  • Amos E. Ajibo
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 272)

Abstract

We give a solvability criterion for a special case of the μ-synthesis problem. That is, we prove the necessity and sufficiency of a condition for the existence of an analytic 2 × 2 matrix-valued function on the disc subject to a bound on the structured singular value and satisfying a finite set of interpolation conditions. To do this we prove a realization theorem for analytic functions from the disc to the tetrablock. We also obtain a solvability criterion for the problem of analytic interpolation from the disc to the tetrablock.

Keywords

Tetrablock interpolation matricial Nevanlinna–Pick problem μ synthesis problem 

Mathematics Subject Classification (2010)

32F45 30E05 93B36 93B50 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Zinaida A. Lykova
    • 1
  • N. J. Young
    • 1
    • 2
  • Amos E. Ajibo
    • 1
  1. 1.School of Mathematics, Statistics and PhysicsNewcastle UniversityNewcastle upon TyneUK
  2. 2.School of MathematicsLeeds UniversityLeedsUK

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