Skip to main content
SpringerLink
Log in

Inequalities for polynomials with a prescribed zero

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

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

References

  1. Blatt, H.-P.: Personal communication

  2. Erdös, P., Turán, P.: On the distribution of roots of polynomials. Ann. of Math.51, 105–119 (1950)

    Google Scholar 

  3. Giroux, A., Rahman, Q.I.: Inequalities for polynomials with a prescribed zero. Trans. Amer. Math. Soc.193, 67–98 (1974)

    Google Scholar 

  4. Halász, G.: On the first and second main theorem in Turán's theory of power sums. Preprint

  5. Kemperman, J.H.B., Lorentz, G.G.: Bounds for incomplete polynomials. Preprint

  6. Lachance, M., Saff, E.B., Varga, R.S.: Bounds for incomplete polynomials vanishing at both endpoints of an interval. In: Proceedings of a conference held at Carnegie-Mellon University (July 10–14, 1978). New York-London: Academic Press (to appear)

  7. Lax, P.D.: Proof of a conjecture of P. Erdös on the derivative of a polynomial. Bull. Amer. Math. Soc.50, 509–513 (1944)

    Google Scholar 

  8. Lorentz, G.G.: Approximation by incomplete polynomials (problems and results). In: Padé and Rational Approximation: Theory and Applications (E.B. Saff and R.S. Varga, eds.). Proceedings of an international symposium (Tampa 1976), pp. 289–302. London-New York: Academic Press 1977

    Google Scholar 

  9. Meinardus, G.: Approximation of Functions: Theory and Numerical Methods, Berlin-Heidelberg-New York: Springer 1967

    Google Scholar 

  10. Pólya, G., Szegö, G.: Problems and Theorems in Analysis I, Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  11. Pommerenke, Ch.: Problems in complex function theory. Bull. London Math. Soc.4, 354–366 (1972)

    Google Scholar 

  12. Rahman, Q.I., Schmeisser, G.: Some inequalities for polynomials with a prescribed zero. Trans. Amer. Math. Soc.216, 91–103 (1976)

    Google Scholar 

  13. Rahman, Q.I., Schmeisser, G.: An extremal problem for polynomials with a prescribed zero. II. Proc. Amer. Math. Soc., (to appear)

  14. Rahman, Q.I., Stenger, F.: An extremal problem for polynomials with a prescribed zero. Proc. Amer. Math. Soc.43, 84–90 (1974)

    Google Scholar 

  15. Saff, E.B., Varga, R.S.: The sharpness of Lorentz's theorem on incomplete polynomials. Trans. Amer. Math. Soc.249, 163–186 (1979)

    Google Scholar 

  16. Saff, E.B., Varga, R.S.: On incomplete polynomials. In: Numerische Methoden der Approximationstheorie, Band 4 (L. Collatz, G. Meinardus, and H. Werner, eds.). Vortragsauszüge einer Tagung (Oberwolfach 1977) pp. 281–298. ISNM Vol. 42. Basel-Stuttgart: Birkhäuser Verlag 1978

    Google Scholar 

  17. Szegö, G.: Orthogonal Polynomials. American Mathematical Society Colloquium Publication Volume XXIII, fourth ed. Providence, Rhode Island: American Mathematical Society 1975

    Google Scholar 

  18. Walsh, J.L.: Interpolation and Approximation by Rational Functions in the Complex Domain. American Mathematical Society Colloquium Publication Volume XX, fifth ed. Providence, Rhode Island: American Mathematical Society 1969

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of South Florida, 33620, Tampa, Florida, USA

    Michael Lachance & Edward B. Saff

  2. Department of Mathematics, Kent State University, 44242, Kent, Ohio, USA

    Richard S. Varga

Authors
  1. Michael Lachance
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Edward B. Saff
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Richard S. Varga
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research was carried out while a Guggenheim Fellow visiting at Oxford Univsity Computing Laboratory, Oxford, England

Research supported in part by the Air Force of Scientific Research and the Department of Energy

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lachance, M., Saff, E.B. & Varga, R.S. Inequalities for polynomials with a prescribed zero. Math Z 168, 105–116 (1979). https://doi.org/10.1007/BF01214190

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01214190

Search

Navigation