Geodesic
Inequalities for Entire Functions of Exponential Type
Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 463-471

Voir la notice de l'article provenant de la source Cambridge University Press

Bernstein's inequality says that if f is an entire function of exponential type τ which is bounded on the real axis then Genchev has proved that if, in addition, hf (π/2) ≤0, where hf is the indicator function of f, then Using a method of approximation due to Lewitan, in a form given by Hörmander, we obtain, to begin, a generalization and a refinement of Genchev's result. Also, we extend to entire functions of exponential type two results first proved for polynomials by Rahman. Finally, we generalize a theorem of Boas concerning trigonometric polynomials vanishing at the origin.
DOI : 10.4153/CMB-1984-073-4
Mots-clés : 30D15 
Frappier, Clément. Inequalities for Entire Functions of Exponential Type. Canadian mathematical bulletin, Tome 27 (1984) no. 4, pp. 463-471. doi: 10.4153/CMB-1984-073-4
@article{10_4153_CMB_1984_073_4,
     author = {Frappier, Cl\'ement},
     title = {Inequalities for {Entire} {Functions} of {Exponential} {Type}},
     journal = {Canadian mathematical bulletin},
     pages = {463--471},
     year = {1984},
     volume = {27},
     number = {4},
     doi = {10.4153/CMB-1984-073-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-073-4/}
}
TY  - JOUR
AU  - Frappier, Clément
TI  - Inequalities for Entire Functions of Exponential Type
JO  - Canadian mathematical bulletin
PY  - 1984
SP  - 463
EP  - 471
VL  - 27
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-073-4/
DO  - 10.4153/CMB-1984-073-4
ID  - 10_4153_CMB_1984_073_4
ER  - 
%0 Journal Article
%A Frappier, Clément
%T Inequalities for Entire Functions of Exponential Type
%J Canadian mathematical bulletin
%D 1984
%P 463-471
%V 27
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1984-073-4/
%R 10.4153/CMB-1984-073-4
%F 10_4153_CMB_1984_073_4

[1] 1. Ankeny, N. C. and Rivlin, T. J., On a theorem of S. Bernstein, Pacific J. Math. 5, (1955), 849-852. Google Scholar | DOI

[2] 2. Bernstein, S. N., Sur Vordre de la meilleure approximation des fonctions continues par les polynömes de degré donné, Mémoire de l'académie Royale de Belgique, vol. 4 (1912), 1-103. Google Scholar

[3] 3. Bernstein, S. N., Sur une propriété des fonctions entières, Comptes rendus de l'académie des sciences, Paris, vol. 176 (1923), 1602-1605. Google Scholar

[4] 4. Boas, R. P., Entire functions, Acad. Press, New York (1954). Google Scholar

[5] 5. Boas, R. P., Inequalities for asymmetric entire functions, Illinois J. Math. 1, (1957), 94-97. Google Scholar | DOI

[6] 6. Boas, R. P., Inequalities for polynomials with a prescribed zero, Studies in mathematical analysis and related topics (Essays in Honour of George Pölya), Stanford Univ. Press, Stanford, Calif. (1962), 42-47. Google Scholar

[7] 7. De Bruijn, N. G., Inequalities concerning polynomials in the complex domain, Nederl. Akad. Wetensch. Proc. 50, (1947), 1265-1272. Google Scholar

[8] 8. Duffin, R. J. and Schaeffer, A. C., Some inequalities concerning functions of exponential type, Bull. Amer. Math. Soc. 43, (1937), 554-556. Google Scholar | DOI

[9] 9. Genchev, T. G., Inequalities for asymmetric entire functions of exponential type, Soviet Math. Dokl., vol. 19 (1978), No. 4, 981-985. Google Scholar

[10] 10. Giroux, A. and Rahman, Q. I., Inequalities for polynomials with a prescribed zero, Trans. Amer. Math. Soc. 193, (1974), 67-98. Google Scholar | DOI

[11] 11. Hörmander, L., Some inequalities for functions of exponential type, Math. Scand. 3, (1955), 21-27. Google Scholar | DOI

[12] 12. Lax, P. D., Proof of a conjecture of P. Erdos on the derivative of a polynomial, Bull. Amer. Math. Soc. 50, (1944), 509-513. Google Scholar | DOI

[13] 13. Lewitan, B. M. Über eine Verallgemeinerung der Ungleichungen von S. Bernstein und H. Bohr. Doklady Akad. Nauk SSSR 15 (1937), 169-172. Google Scholar

[14] 14. Rahman, Q. I., Functions of exponential type, Trans. Amer. Math. Soc. 135, (1969), 295-309. Google Scholar | DOI

[15] 15. Szegö, G., Űber einen Satz des Herrn Serge Bernstein, Schr. Königsb. gelehrt. Ges., Vol, 22 (1928), 59-70. Google Scholar

Cité par Sources :