Skip to main content

An Indefinite Analog of Sarason’s Generalized Interpolation Theorem

  • Chapter
  • First Online:
Function Spaces, Theory and Applications

Part of the book series: Fields Institute Communications ((FIC,volume 87))

  • 196 Accesses

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. Daniel Alpay, Aad Dijksma, and James Rovnyak, On Nudel\('\)man’s problem and indefinite interpolation in the generalized Schur and Nevanlinna classes, Complex Anal. Oper. Theory 14 (2020), no. 1, Art. 25, 30. MR 4060499

    Google Scholar 

  2. Daniel Alpay, Aad Dijksma, James Rovnyak, and Hendrik de Snoo, Schur functions, operator colligations, and reproducing kernel Pontryagin spaces, Operator Theory: Advances and Applications, vol. 96, Birkhäuser Verlag, Basel, 1997. MR 1465432

    Google Scholar 

  3. Rodrigo Arocena, Tomas Ya. Azizov, Aad Dijksma, and Stefania A. M. Marcantognini, On commutant lifting with finite defect. II, J. Funct. Anal. 144 (1997), no. 1, 105–116. MR 1430717

    Google Scholar 

  4. J. A. Ball and V. Bolotnikov, de Branges-Rovnyak spaces: basics and theory, Operator theory (D. Alpay, ed.), Springer, Basel, 2015, pp. 631–679.

    Google Scholar 

  5. Louis de Branges and James Rovnyak, Canonical models in quantum scattering theory, Perturbation Theory and its Applications in Quantum Mechanics (Proc. Adv. Sem. Math. Res. Center, U.S. Army, Theoret. Chem. Inst., Univ. of Wisconsin, Madison, Wis., 1965), Wiley, New York, 1966, pp. 295–392. MR 0244795

    Google Scholar 

  6. ——, Square summable power series, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1966. MR 0215065

    Google Scholar 

  7. Emmanuel Fricain and Javad Mashreghi, The theory of\(\mathcal H\)(b) spaces. Vol. 1, New Mathematical Monographs, vol. 20, Cambridge University Press, Cambridge, 2016. MR 3497010

    Google Scholar 

  8. ——, The theory of\(\mathcal {H}(b)\)spaces. Vol. 2, New Mathematical Monographs, vol. 21, Cambridge University Press, Cambridge, 2016. MR 3617311

    Google Scholar 

  9. Stephan Ramon Garcia, Javad Mashreghi, and William T. Ross, Introduction to model spaces and their operators, Cambridge Studies in Advanced Mathematics, vol. 148, Cambridge University Press, Cambridge, 2016. MR 3526203

    Google Scholar 

  10. N. K. Nikol\('\)skiı̆, Treatise on the shift operator, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 273, Springer-Verlag, Berlin, 1986, Spectral function theory, With an appendix by S. V. Hruščev [S. V. Khrushchëv] and V. V. Peller, Translated from the Russian by Jaak Peetre. MR 827223

    Google Scholar 

  11. Donald Sarason, Generalized interpolation in\(H^{\infty }\), Trans. Amer. Math. Soc. 127 (1967), 179–203. MR 208383

    Google Scholar 

  12. ——, Shift-invariant spaces from the Brangesian point of view, The Bieberbach conjecture (West Lafayette, Ind., 1985), Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 153–166. MR 875239

    Google Scholar 

  13. ——, Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Notes in the Mathematical Sciences, vol. 10, John Wiley & Sons, Inc., New York, 1994, A Wiley-Interscience Publication. MR 1289670

    Google Scholar 

  14. Morris Schreiber, A functional calculus for general operators in Hilbert space, Trans. Amer. Math. Soc. 87 (1958), 108–118. MR 99601

    Google Scholar 

  15. Béla Sz.-Nagy and Ciprian Foiaş, Sur les contractions de l’espace de Hilbert. III, Acta Sci. Math. (Szeged) 19 (1958), 26–45. MR 103418

    Google Scholar 

  16. ——, Harmonic analysis of operators on Hilbert space, North-Holland Publishing Co., Amsterdam-London; American Elsevier Publishing Co., Inc., New York; Akadémiai Kiadó, Budapest, 1970, Translated from the French and revised. MR 0275190

    Google Scholar 

  17. Dan Timotin, A short introduction to de Branges–Rovnyak spaces, Invariant subspaces of the shift operator, Contemp. Math., vol. 638, Amer. Math. Soc., Providence, RI, 2015, pp. 21–38. MR 3309347

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to James Rovnyak .

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

Cite this chapter

Rovnyak, J. (2023). An Indefinite Analog of Sarason’s Generalized Interpolation Theorem. In: Binder, I., Kinzebulatov, D., Mashreghi, J. (eds) Function Spaces, Theory and Applications. Fields Institute Communications, vol 87. Springer, Cham. https://doi.org/10.1007/978-3-031-39270-2_2

Download citation

Publish with us

Policies and ethics