Skip to main content
SpringerLink
Log in

Two new characterizations of carleson-newman Blaschke products

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We present an extension of a result of Vasyunin by giving a characterization of finite products of interpolating Blaschke products B in terms of the minorization of B(z) by the distance of z to the zeros of B. We also characterize those Blaschke products that satisfy the hereditary weak embedding property.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. B. Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, 96, Academic Press, New York-London, 1981, xvi+467 pp.

    MATH  Google Scholar 

  2. P. Gorkin and R. Mortini, Interpolating Blaschke products and factorization in Douglas algebras, The Michigan Mathematical Journal 38 (1991), 147–160.

    Article  MATH  MathSciNet  Google Scholar 

  3. P. Gorkin, K. Izuchi and R. Mortini, Higher order hulls in H ∞ II, Journal of Functional Analysis 177 (2000), 107–129.

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Gorkin, H.-M. Lingenberg and R. Mortini, Homeomorphic disks in the spectrum of ∞, Indiana University Mathematics Journal 39 (1990), 961–983.

    Article  MathSciNet  Google Scholar 

  5. P. Gorkin, R. Mortini and N. Nikolski, Norm controlled inversions and a corona theorem for ∞-quotient algebras, Journal of Functional Analysis 255 (2008), 854–876.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. Guillory, K. Izuchi and D. Sarason, Interpolating Blaschke products and division in Douglas algebras, Mathematical Proceedings of the Royal Irish Academy 84 (1984), 1–7.

    MATH  MathSciNet  Google Scholar 

  7. K. Hoffman, Banach Spaces of Analytic Functions, Reprint of the 1962 original, Dover Publications, Inc., New York, 1988.

    MATH  Google Scholar 

  8. K. Hoffman, Bounded analytic functions and Gleason parts, Annals of Mathematics 86 (1967), 74–111.

    Article  MathSciNet  Google Scholar 

  9. A. Kerr-Lawson, Some lemmas on interpolating Blaschke products and a correction, Canadian Journal of Mathematics 21 (1969), 531–534.

    MATH  MathSciNet  Google Scholar 

  10. L. Laroco, Stable rank and approximation theorems for H ∞, Transactions of the American Mathematical Society 327 (1991), 815–832.

    Article  MATH  MathSciNet  Google Scholar 

  11. G. McDonald and C. Sundberg, Toeplitz operators on the disk, Indiana University Mathematics Journal 28 (1979), 595–611.

    Article  MATH  MathSciNet  Google Scholar 

  12. P.J. McKenna, Discrete Carleson measures and some interpolation problems, TheMichigan Mathematical Journal 24 (1977), 311–319.

    Article  MATH  MathSciNet  Google Scholar 

  13. R. Mortini, Interpolating sequences in the spectrum of H ∞, I, Proceedings of the American Mathematical Society 128 (1999), 1703–1710.

    Article  MathSciNet  Google Scholar 

  14. R. Mortini and A. Nicolau, Frostman shifts of inner functions, Journal d’Analyse Mathématique 92 (2004), 285–326.

    Article  MATH  MathSciNet  Google Scholar 

  15. N. K. Nikolski, Treatise on the Shift Operator. Spectral Function Theory, With an appendix by S. V. Hruščev [S. V. Khrushchev] and V. V. Peller, Translated from the Russian by Jaak Peetre, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 273, Springer-Verlag, Berlin, 1986.

    Google Scholar 

  16. N. K. Nikolski, Operators, Functions, and Systems: An Easy Reading, Vol. 1 and Vol. 2, Model Operators and Systems, Mathematical Surveys and Monographs, 93, American Mathematical Society, Providence, RI, 2002.

    Google Scholar 

  17. N. K. Nikolski and S. V. Khrushchëv, A functional model and some problems of the spectral theory of functions, (Russian) Trudy Matematicheskogo Instituta Imeni V. A. Steklova 176 (1987), 97–210; translated in Proceedings of the Steklov Institute of Mathematics (1988), no. 3, 101–214.

    Google Scholar 

  18. N. K. Nikolski and A. Volberg, Tangential and approximate free interpolation, in Analysis and Partial Differential Equations, Lecture Notes in Pure and Applied Mathematics, 122, Dekker, New York, 1990, pp. 277–299.

    Google Scholar 

  19. V. Tolokonnikov, Blaschke products satisfying the Carleson-Newman conditions and ideals of the algebra H ∞, Journal of Soviet Mathematics 42 (1988) 1603–1610.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bucknell University, Lewisburg, PA, 17837, USA

    Pamela Gorkin

  2. Laboratoire de Mathématiques et Applications de Metz, UMR 7122, Université Paul Verlaine Ile du Saulcy, F-57045, Metz, France

    Raymond Mortini

Authors
  1. Pamela Gorkin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Raymond Mortini
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pamela Gorkin.

Additional information

Dedicated to the memory of D.J. Newman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gorkin, P., Mortini, R. Two new characterizations of carleson-newman Blaschke products. Isr. J. Math. 177, 267–284 (2010). https://doi.org/10.1007/s11856-010-0046-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-010-0046-5

Keywords

Search

Navigation