Advertisement

Quelques aspects de la theorie analytique des polynomes II

  • A. Durand
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 1415)

Keywords

Extremal Problem Nous Allons Prescribe Zero Peut Supposer Assertion Suivante 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. AZIZ [1982]: Inequalities for polynomials with a prescribed zero; Canad. J. Math. 34 (1982), 737–740.MathSciNetCrossRefzbMATHGoogle Scholar
  2. A. AZIZ, Q.G. MOHAMMAD [1980]: Simple proof of a theorem of Erdös and Lax; Proc. Amer. Math. Soc. 80 (1980), 119–122.MathSciNetzbMATHGoogle Scholar
  3. E. BELLER, D.J. NEWMAN [1971]: An ℓ1 extremal problem for polynomials; Proc. Amer. Math. Soc. 29 (1971), 474–481.MathSciNetzbMATHGoogle Scholar
  4. R.P. BOAS [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
  5. D.W. BOYD [1980]: Reciprocal polynomials having small measure; Math. Comp. 35 (1980), 1361–1377.MathSciNetCrossRefzbMATHGoogle Scholar
  6. F.P. CALLAHAN [1959]: An extremal problem for polynomials; Proc. Amer. Math. Soc. 10 (1959), 754–755.MathSciNetCrossRefzbMATHGoogle Scholar
  7. J.G. van der CORPUT, C. VISSER [1946]: Inequalities concerning polynomials and trigonometric polynomials; Nederl. Akad. Wetensch. Proc. 49 (1946), 383–392.MathSciNetzbMATHGoogle Scholar
  8. K.K. DEWAN, N.K. GOVIL [1983]: Some integral inequalities for polynomials; Indian J. Pure. Appl. Math. 14 (1983), 440–443.MathSciNetzbMATHGoogle Scholar
  9. J.D. DONALDSON, Q.I. RAHMAN [1972]: Inequalities for polynomials with a prescribed zero; Pacific J. Math. 41 (1972), 375–378.MathSciNetCrossRefzbMATHGoogle Scholar
  10. R.L. DUNCAN [1966]: Some inequalities for polynomials; Amer. Math. Monthly 73 (1966), 58–59.MathSciNetCrossRefzbMATHGoogle Scholar
  11. M. FAIT, J. STANKIEWICZ, J. ZYGMUNT [1975]: On some classes of polynomials; Ann. Univ. Mariae Curie-Sklodowska Sect. A 29 (1975), 61–67.MathSciNetzbMATHGoogle Scholar
  12. K. FAN, O. TAUSSKY, J. TODD [1955]: An algebraic proof of the isoperimetric inequality for polygons; J. Washington Acad. Sci. 45 (1955), 339–342.MathSciNetGoogle Scholar
  13. A. GIROUX, Q.I. RAHMAN [1974]: Inequalities for polynomials with a prescribed zero; Trans. Amer. Math. Soc. 193 (1974), 67–98.MathSciNetCrossRefzbMATHGoogle Scholar
  14. G.M. GOLUZIN [1969]: Geometric theory of functions of a complex variable; Translations of Math. Monographs, vol. 26, Amer. Math. Soc. Providence R.I. 1969.Google Scholar
  15. J.V. GONCALVES [1950]: L'inégalité de W. Specht; Univ. Lisboa Revista Fac. de Ciências (2) ser A (1950), 167–171.Google Scholar
  16. N.K. GOVIL, Q.I. RAHMAN [1969]: Functions of exponential type not vanishing in a half-plane and related polynomials; Trans. Amer. Math. Soc. 137 (1969), 501–517.MathSciNetCrossRefzbMATHGoogle Scholar
  17. F. HOLLAND [1973]: Some extremum problems for polynomials with positive real part; Bull. London Math. Soc. 5 (1973), 54–58.MathSciNetCrossRefzbMATHGoogle Scholar
  18. V.K. JAIN [1977]: Some inequalities for polynomials; Glasnik Mat. Ser III. 12 (1977), 263–269.MathSciNetzbMATHGoogle Scholar
  19. J.P. KAHANE [1980]: Sur les polynômes à coefficients unimodulaires; Bull. London Math. Soc. 12 (1980), 321–342.MathSciNetCrossRefzbMATHGoogle Scholar
  20. M. LACHANCE, E.B. SAFF, R.S. VARGA [1979]: Inequalities for polynomials with a prescribed zero; Math. Z. 168 (1979), 105–116.MathSciNetCrossRefzbMATHGoogle Scholar
  21. P.D. LAX [1944]: Proof of a conjecture of P. Erdös on the derivative of a polynomial; Bull. Amer. Math. Soc. 50 (1944), 509–513.MathSciNetCrossRefzbMATHGoogle Scholar
  22. K. MAHLER [1960]: An application of Jensen's formula to polynomials; Mathematika 7 (1960), 98–100.MathSciNetCrossRefzbMATHGoogle Scholar
  23. E. MAKAI [1958]: On a maximum problem; Acta Math. Acad. Sci. Hungar. 9 (1958), 105–110.MathSciNetCrossRefzbMATHGoogle Scholar
  24. M.A. MALIK [1963]: An inequality for polynomials; Canad. Math. Bull. 6 (1963), 65–69.MathSciNetCrossRefzbMATHGoogle Scholar
  25. L. MIRSKY [1962]: Estimates of zeros of a polynomial; Proc. Cambridge Philos. Soc. 58 (1962), 229–234.MathSciNetCrossRefzbMATHGoogle Scholar
  26. H.P. MULHOLLAND [1956]: On two extremum problems for polynomials on the unit circle; J. London Math. Soc. 31 (1956), 191–199.MathSciNetCrossRefzbMATHGoogle Scholar
  27. D.J. NEWMAN [1962]: Problem 5040; Amer. Math. Monthly 69 (1962), 670.MathSciNetCrossRefGoogle Scholar
  28. P.J. O'HARA [1973]: Another proof of Bernstein's theorem; Amer. Math. Monthly 80 (1973), 673–674.MathSciNetCrossRefzbMATHGoogle Scholar
  29. A.M. OSTROWSKI [1960]: On an inequality of J. Vicente Gonçalves; Univ. Lisboa Revista Fac. de Ciências (2) ser A (1960), 115–119.Google Scholar
  30. G. POLYA, G. SZEGÖ [1976]: Problems and theorems in analysis I,II; Springer Verlag; Berlin, Heidelberg 1976.CrossRefzbMATHGoogle Scholar
  31. Q.I. RAHMAN [1961]: Some inequalities for polynomials and related entire functions; Illinois J. Math. 5 (1961), 144–151.MathSciNetzbMATHGoogle Scholar
  32. Q.I. RAHMAN [1963]: Inequalities concerning polynomials and trigonometric polynomials; J. Math. Anal. Appl. 6 (1963), 303–324.MathSciNetCrossRefzbMATHGoogle Scholar
  33. Q.I. RAHMAN [1964]: Some inequalities for polynomials and related entire functions II; Canad. Math. Bull. 7 (1964), 573–595.MathSciNetCrossRefzbMATHGoogle Scholar
  34. Q.I. RAHMAN [1965]: L2 inequalities for polynomials and asymetric entire functions; Indian J. Math. 7 (1965), 67–72.MathSciNetGoogle Scholar
  35. Q.I. RAHMAN [1968]: Applications of functional analysis to extremal problems for polynomials; Les Presses de l'Université de Montréal, vol. no 29, Montréal 1968.Google Scholar
  36. Q.I. RAHMAN, F. STENGER [1974]: An extremal problem for polynomials with a prescribed zero; Proc. Amer. Math. Soc. 43 (1974), 84–90.MathSciNetCrossRefzbMATHGoogle Scholar
  37. Q.I. RAHMAN, G. SCHMEISSER [1976]: Some inequalities for polynomials with a prescribed zero; Trans. Amer. Math Soc. 216 (1976), 91–103.MathSciNetCrossRefzbMATHGoogle Scholar
  38. Q.I. RAHMAN, G. SCHMEISSER [1979]: An extremal problem for polynomials with a prescribed zero II; Proc. Amer. Math. Soc. 73 (1979), 375–378.MathSciNetCrossRefzbMATHGoogle Scholar
  39. M. RIESZ [1914]: Eine trigonometrische Interpolationsformel und einige Ungleichungen für Polynome; Jahresbericht der Deutschen Math. Vereinigung 23 (1914), 354–368.zbMATHGoogle Scholar
  40. W.W. ROGOSINSKI [1955]: Some elementary inequalities for polynomials; Math. Gaz 39 (1955), 7–12.MathSciNetCrossRefzbMATHGoogle Scholar
  41. W. RUDIN [1975]: Analyse réelle et complexe. Masson et Cie. Paris 1975.Google Scholar
  42. H.S. SHAPIRO [1961]: On a class of extremal problems for polynomials in the unit circle; Portugaliae Math. 20 (1961), 67–93.MathSciNetzbMATHGoogle Scholar
  43. J.R. SLAGLE [1968]: Generalizations of a complex analogue of the real Tchebichev polynomial theorem; Amer. Math. Monthly 75 (1968), 58–59.MathSciNetCrossRefzbMATHGoogle Scholar
  44. C. VISSER [1945]: A simple proof of certain inequalities concerning polynomials; Nederl. Akad. Wetensch. Proc. 47 (1945), 276–281.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • A. Durand
    • 1
  1. 1.Département de MathématiquesU.E.R. des SciencesLimoges Cedex

Personalised recommendations