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Representation Formulas for Hardy Space Functions Through the Cuntz Relations and New Interpolation Problems

  • Daniel AlpayEmail author
  • Palle Jorgensen
  • Izchak Lewkowicz
  • Itzik Marziano
Chapter

Abstract

We introduce connections between the Cuntz relations and the Hardy space H 2 of the open unit disk \(\mathbb{D}\). We then use them to solve a new kind of multipoint interpolation problem in H 2, where, for instance, only a linear combination of the values of a function at given points is preassigned, rather than the values at the points themselves.

Keywords

Cuntz Relations Tangential Interpolation Problem Open Unit Disk Multipoint Interpolation Schur Functions 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The work of the first three authors was supported in part by the Bi-national Science Foundation grant 2010117. D. Alpay thanks the Earl Katz family for endowing the chair which supported his research. The work was done in part while the second named author visited Department of Mathematics, Ben Gurion University of the Negev, supported by a BGU distinguished visiting scientist program. Support and hospitality is much appreciated. We acknowledge discussions with colleagues there, and in the US, Dorin Dutkay, Myung-Sin Song, and Erin Pearse.

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Copyright information

© Springer New York 2013

Authors and Affiliations

  • Daniel Alpay
    • 1
    Email author
  • Palle Jorgensen
    • 2
  • Izchak Lewkowicz
    • 3
  • Itzik Marziano
    • 1
  1. 1.Department of MathematicsBen Gurion University of the NegevBe’er ShevaIsrael
  2. 2.Department of MathematicsThe University of IowaIowa CityUSA
  3. 3.Department of Electrical EngineeringBen Gurion University of the NegevBe’er ShevaIsrael

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