A complex analogue of the Rolle theorem and polynomial envelopes of irreducible differential equations in the complex domain

Journal of the London Mathematical Society

Volumn 56, Issue 2, 1997, Pages 305-319

  Novikov, D ^a   Yakovenko, S ^a  

^a WEIZMANN INSTITUTE OF SCIENCE   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0040657057     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/S002461079700536X     Document Type: Article

References (12)

1. S. BERNSTEIN, 'Leçons sur les propriétés extrémales et la meilleure approximation des fonctions analytiques d'une variable réelle', Paris, 1926; reprinted in S. BERNSTEIN and C. DE LA VALLÉE POUSSIN, l'Approximation (Chelsea, Bronx, 1970).
2. YU. IL'YASHENKO and S. YAKOVENKO, 'Counting the number of zeros of analytic functions satisfying linear ordinary differential equations', J. Differential Equations 126 (1996) 87-105.
3. YU. IL'YASHENKO and S. YAKOVENKO, 'Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear differential equations with an irreducible monodromy group', Invent. Math. 121 (1995) 613-650.
4. A. KHOVANSKIǏ, Fewnomials, American Mathematical Society Colloquium Publications (American Mathematical Society, Providence, 1991).
5. D. NOVIKOV and S. YAKOVENKO, 'Une borne simplement exponentielle pour le nombre de zéros réels isolés des intégrales complètes abéliennes', C.R. Acad. Sci. Paris Sér. I 320 (1995) 853-858.
6. D. NOVIKOV and S. YAKOVENKO, 'Simple exponential estimate for the number of zeros of complete Abelian integrals', Ann. Inst. Fourier (Grenoble) 45 (1995) 897-927.
7. G. PETROV, 'On the number of zeros of complete Abelian integrals', Functional Anal. Appl. 18 (1984) 73-74; 'Complex zeros of an elliptic integral', ibid. 20 (1986) 46-49; 'Nonoscillation of elliptic integrals', ibid. 24 (1990) 45-50.
8. G. PETROV, 'On the number of zeros of complete Abelian integrals', Functional Anal. Appl. 18 (1984) 73-74; 'Complex zeros of an elliptic integral', ibid. 20 (1986) 46-49; 'Nonoscillation of elliptic integrals', ibid. 24 (1990) 45-50.
9. G. PETROV, 'On the number of zeros of complete Abelian integrals', Functional Anal. Appl. 18 (1984) 73-74; 'Complex zeros of an elliptic integral', ibid. 20 (1986) 46-49; 'Nonoscillation of elliptic integrals', ibid. 24 (1990) 45-50.
10. M. VOORHOEVE, 'On the oscillation of exponential polynomials', Math. Z. 151 (1976) 277-294.
11. M. VOORHOEVE, 'A generalization of Descartes' rule', J. London Math. Soc. (2) 20 (1979) 446-456.
12. S. YAKOVENKO, 'Abelian integrals as rational envelopes', Nonlinearity 7 (1994) 1237-1250.