On Nontangential Limits and Shift Invariant Subspaces

  • John R. AkeroydEmail author
  • John B. Conway
  • Liming Yang


In 1998, Conway and Yang wrote a paper (Holomorphic spaces, MSRI Publications, vol 33, pp 201–209, 1998) in which they posed a number of open questions regarding the shift on \(P^t(\mu )\) spaces. A few of these have been completely resolved, while at least one remains wide open. In this paper, we review some of the solutions, mention some alternate approaches and discuss further the problem that remains unsolved.


Nontangential limits Shift invariant subspaces Bounded point evaluations 

Mathematics Subject Classification

Primary 47A15 Secondary 30C85 31A15 46E15 47B38 



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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • John R. Akeroyd
    • 1
    Email author
  • John B. Conway
    • 2
  • Liming Yang
    • 3
  1. 1.Department of MathematicsUniversity of ArkansasFayettevilleUSA
  2. 2.Department of MathematicsThe George Washington UniversityWashingtonUSA
  3. 3.Department of MathematicsVirginia Polytechnic and State UniversityBlacksburgUSA

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