Skip to main content
SpringerLink
Log in

Quelques aspects de la theorie analytique des polynomes I

  • Chapter
  • First Online:
Cinquante Ans de Polynômes Fifty Years of Polynomials

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1415))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • V.V. ARESTOV [1980]: Inequality of various metrics for trigonometric polynomials; Mat. Zametki 27 (1980), no 4, 539–547,669. (Math. Notes 27 (1980), 265–269).

    MathSciNet  MATH  Google Scholar 

  • A.A. BALKEMA, R. TIJDEMAN [1973]: Some estimates in the theory of exponential sums; Acta Math. Acad. Sci. Hung. 24 (1973), 115–133.

    Article  MathSciNet  MATH  Google Scholar 

  • E. BELLER [1971]: Polynomial extremal problems in Lp; Proc. Amer. Math. Soc. 30 (1971), 249–259.

    MathSciNet  MATH  Google Scholar 

  • E. BELLER, D.J. NEWMAN [1973]: An extremal problem for the geometric mean of polynomials; Proc. Amer. Math. Soc. 39 (1973), 313–317.

    Article  MathSciNet  MATH  Google Scholar 

  • R.P. BOAS Jr [1962]: Inequalities for polynomials with a prescribed zero; Studies in mathematical analysis and related topics, p. 42–47. Stanford Univ. Press, Stanford, Calif. 1962.

    Google Scholar 

  • J. DIEUDONNE [1934]: Sur quelques applications de la théorie des fonctions bornées aux polynômes dont toutes les racines sont dans un domaine circulaire donné; Actualités Sci. Ind. no 114, Hermann, Paris 1934.

    Google Scholar 

  • J. DIEUDONNE [1968]: Calcul infinitésimal; Hermann, Paris 1968.

    MATH  Google Scholar 

  • G.T. FIELDING [1970]: The expected value of the integral around the unit circle of a certain class of polynomials; Bull. London Math. Soc. 2 (1970), 301–306.

    Article  MathSciNet  MATH  Google Scholar 

  • D. GAIER [1970]: Bemerkungen zum Turánschen Lemma; Abh. Math. Sem. Univ. Hamburg 35 (1970), 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  • G.M. GOLUZIN [1969]: Geometric theory of functions of a complex variable; Translations of Math. Mongraphs, vol. 26, Amer. Math. Soc. Providence R.I. 1969.

    MATH  Google Scholar 

  • G.H. HARDY, J.E. LITTLEWOOD, G. POLYA [1952]: Inequalities; Cambridge Univ. Press 1952.

    Google Scholar 

  • C. HYLTEN-CAVALLIUS [1955]: Some extremal problems for trigonometrical and complex polynomials; Math. Scand. 3 (1955), 5–20.

    MathSciNet  MATH  Google Scholar 

  • J.E. LITTLEWOOD [1962]: On the mean values of certain trigonometrical polynomials (II); Illinois J. of Math. 6 (1962), 1–39.

    MathSciNet  MATH  Google Scholar 

  • J.E. LITTLEWOOD [1966]: On polynomials ; J. London Math. Soc. 41 (1966), 367–376.

    Article  MathSciNet  MATH  Google Scholar 

  • K. MAHLER [1963]: On two extremum properties of polynomials; Illinois J. of Math. 7 (1963), 681–701.

    MathSciNet  MATH  Google Scholar 

  • A. MATE, P.G. NEVAI [1980]: Bernstein's inequality in Lp for 0 < p < 1 and (C,1) bounds for orthogonal polynomials; Ann. of Math. 111 (1980), 145–154.

    Article  MathSciNet  MATH  Google Scholar 

  • D.S. MITRINOVIC [1970]: Analytic inequalities; Springer-Verlag, Berlin, Heidelberg 1970.

    Book  MATH  Google Scholar 

  • R.J. NESSEL, G. WILMES [1978]: Nikolskii-type inequalities for trigonometric polynomials and entire functions of exponential type; J. Austral. Math. Soc. 25 (ser. A) (1978), 7–18.

    Article  MathSciNet  MATH  Google Scholar 

  • D.J. NEWMAN [1965]: An L1 extremal problem for polynomials; Proc. Amer. Math. Soc. 16 (1965), 1287–1290.

    MathSciNet  MATH  Google Scholar 

  • M. NEWMAN [1967]: The coefficients of the powers of a polynomial; J. Res. Nat. Bur. Standards Sect. B. 71 B (1967), 9–10.

    Article  MathSciNet  MATH  Google Scholar 

  • G. POLYA, G. SZEGÖ [1976]: Problems and theorems in analysis I et II; Springer Verlag, Berlin, Heidelberg 1976.

    Book  MATH  Google Scholar 

  • Q.I. RAHMAN [1969]: Some inequalities concerning functions of exponential type; Trans. Amer. Math. Soc. 135 (1969), 281–293.

    Article  MathSciNet  MATH  Google Scholar 

  • Q.I. RAHMAN, J. STANKIEWICZ [1974]: Differential inequalities and local valency; Pacific J. Math. 54 (1974), 165–181.

    Article  MathSciNet  MATH  Google Scholar 

  • Z. RUBINSTEIN [1965]: Some results in the location of zeros of polynomials; Pacific J. Math. 15 (1965), 1391–1395.

    Article  MathSciNet  MATH  Google Scholar 

  • Z. RUBINSTEIN [1965 a]: Some inequalities for polynomials and their zeros; Proc. Amer. Math. Soc. 16 (1965), 72–75.

    Article  MathSciNet  MATH  Google Scholar 

  • Z. RUBINSTEIN [1980]: Some properties of two analytic functions associated with complex polynomials; J. Math. Anal. Appl. 74 (1980), 464–474.

    Article  MathSciNet  MATH  Google Scholar 

  • Z. RUBINSTEIN, J.L. WALSH [1969]: Extension and some applications of the coincidence theorems; Trans. Amer. Math. Soc. 146 (1969), 413–427.

    Article  MathSciNet  MATH  Google Scholar 

  • S.O. SINANJAN [1963]: An extremal problem for polynomials; Uspehi Mat. Nauk. 18 (1963), 159–161.

    MathSciNet  Google Scholar 

  • L.R. SONS [1975]: Polynomial growth along Jordan arcs; Math. Z. 141 (1975), 1–8.

    Article  MathSciNet  MATH  Google Scholar 

  • G. SZEGÖ, A. ZYGMUND [1954]: On certain mean values of polynomials; J. Analyse Math. 3 (1954), 225–244.

    Article  MathSciNet  MATH  Google Scholar 

  • J.L. WALSH [1960]: Interpolation and approximation by rational functions in the complex domain; Amer. Math. Soc. Colloquium Publications, vol. XX, Providence R.I. 1960.

    Google Scholar 

  • Z. ZIEGLER [1977]: Minimizing the Lp,∞-distorsion of trigonometric polynomials; J. Math. Anal. Appl. 61 (1977), 426–431.

    Article  MathSciNet  MATH  Google Scholar 

  • A. ZYGMUND [1968]: Trigonometric series, vol. I,II; Cambridge Univ. Press 1968.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département De Mathématiques, U.E.R. Des Sciences, 123 rue Albert Thomas, 87060, Limoges Cedex

    A. Durand

Authors
  1. A. Durand
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michel Langevin Michel Waldschmidt

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag

About this chapter

Cite this chapter

Durand, A. (1990). Quelques aspects de la theorie analytique des polynomes I. In: Langevin, M., Waldschmidt, M. (eds) Cinquante Ans de Polynômes Fifty Years of Polynomials. Lecture Notes in Mathematics, vol 1415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084877

Download citation

  • DOI: https://doi.org/10.1007/BFb0084877

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52190-7

  • Online ISBN: 978-3-540-46919-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation