Skip to main content

Frames of Iterations and Vector-Valued Model Spaces

  • Chapter
  • First Online:
Sampling, Approximation, and Signal Analysis

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Aldroubi, C. Cabrelli, A.F. Çakmak, U. Molter, A. Petrosyan, Iterative actions of normal operators. J. Funct. Anal. 272, 1121–1146 (2017)

    Article  MathSciNet  Google Scholar 

  2. A. Aldroubi, C. Cabrelli, U. Molter, S. Tang, Dynamical sampling. Appl. Comput. Harmon. Anal. 42, 378–401 (2017)

    Article  MathSciNet  Google Scholar 

  3. A. Beurling, On two problems concerning linear transformations in Hilbert space. Acta Math. 81, 239–255 (1949)

    Article  MathSciNet  Google Scholar 

  4. M. Bownik, The structure of shift-invariant subspaces of \(L^2 (\mathbb {R} )^n\). J. Funct. Anal. 177(2), 282–309 (2000)

    Google Scholar 

  5. C. Cabrelli, U. Molter, V. Paternostro, F. Philipp, Dynamical sampling on finite index sets. J. d’Analyse Mathématique 140, 637–667 (2019)

    Article  MathSciNet  Google Scholar 

  6. C. Cabrelli, U. Molter, D. Suárez, Multi-orbital frames through model spaces. Complex Anal. Oper. Theory 15, 16, 1–22 (2021)

    MathSciNet  Google Scholar 

  7. L. Carleson, Interpolation by bounded analytic functions and the corona problem. Ann. Math. 76, 547–559 (1962)

    Article  MathSciNet  Google Scholar 

  8. O. Christensen, M. Hasannasab, F. Philipp, Frame properties of operator orbits. Math. Nachr. 293, 52–66 (2020)

    Article  MathSciNet  Google Scholar 

  9. R.G. Douglas, P.S. Muhly, C. Pearcy, Lifting commuting operators. Michigan Math. J. I5, 385–395 (1968)

    MathSciNet  Google Scholar 

  10. P.A. Fuhrmann, On the corona theorem and its applications to spectral problems in Hilbert space. T.A.M.S. 132(1), 55–66 (1968)

    Google Scholar 

  11. J.B. Garnett, Bounded Analytic Functions. Graduate Texts in Mathematics, vol. 236, Revised edn. (Springer, Berlin, 2006)

    Google Scholar 

  12. P.R. Halmos, Shifts on Hilbert spaces. J. Reine Angew. Math. 208, 102–112 (1961)

    Article  MathSciNet  Google Scholar 

  13. H. Helson, Lectures on Invariant Subspaces (Academic Press, New York, 1964)

    Google Scholar 

  14. H. Helson, D. Lowdenslager, Invariant subspaces, in Proc. Int. Sympos. Linear Spaces (Jerusalem, 1960), (Macmillan (Pergamon), New York, 1961), pp. 251–262

    Google Scholar 

  15. R.V. Kadison, Diagonalizing matrices. American J. Math. 106(6), 1451–1468 (1984)

    Article  MathSciNet  Google Scholar 

  16. P.D. Lax, Translation invariant spaces. Acta Math. 101, 163–178 (1959)

    Article  MathSciNet  Google Scholar 

  17. J. Nagata, Modern Dimension Theory (Heldermann Verlag, Berlin, 1964)

    Google Scholar 

  18. T.P. Srinivasan, Double invariant subspaces. Pacific J. Math. 14(2), 701–707 (1964)

    Article  MathSciNet  Google Scholar 

  19. V.A. Tolokonnikov, Estimates in the Carleson corona theorem, ideals of the algebra \(H^\infty \), a problem of Sz.-Nagy. Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 113, 178–198, 267 (1981). Investigations on linear operators and the theory of functions, XI

    Google Scholar 

  20. K. Zhu, Operator Theory in Function Spaces. Mathematical Surveys and Monographs, vol. 138, 2nd edn. (AMS, Providence,2007)

    Google Scholar 

Download references

Acknowledgements

We are grateful to E. Andruchow for bringing Kadison’s paper [15] to our attention.

The research of the authors is partially supported by grants UBACyT 20020170100430BA, PICT 2018-3399 (ANPCyT), and CONICET PIP 11220150100355.

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Cabrelli, C., Molter, U., Suárez, D. (2023). Frames of Iterations and Vector-Valued Model Spaces. In: Casey, S.D., Dodson, M.M., Ferreira, P.J.S.G., Zayed, A. (eds) Sampling, Approximation, and Signal Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-41130-4_12

Download citation

Publish with us

Policies and ethics