Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-27T16:12:49.204Z Has data issue: false hasContentIssue false
  • English
  • Français

Some precisions on the Fourier-Borel transform and infinite order differential equations

Published online by Cambridge University Press:  18 May 2009

Lawrence Gruman
Lawrence Gruman
Affiliation:
Tulane University, New Orleans, LA 70118, U.S.A
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f(z) be an entire function (of several variables). We define the function

which is increasing. The orderof f(z) is the constant (perhaps infinite)

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 14 , Issue 2 , September 1973 , pp. 161 - 167
Copyright
Copyright © Glasgow Mathematical Journal Trust 1973

References

REFERENCES

1.Gruman, L., The growth of entire solutions of differential equations of finite and infinite order, Ann. Inst. Fourier 22 (1972).CrossRefGoogle Scholar
2.Hörmander, L., An introduction to complex analysis in several variables(Van Nostrand, 1966).Google Scholar
3.Lelong, P., Fonctionelles analytiques etfonctions entieres (n variables) (Montreal, 1968).Google Scholar
4.Levin, B. Ja., Distribution of zeros of entire functions, Amer. Math. Soc. Translations of Mathematical Monographs 5 (Providence, R.I., 1964).CrossRefGoogle Scholar
5.Martineau, A., Indicatrices de croissance des fonctions entières de N variables, Inventiones Math. 2 (1966), 81–86.CrossRefGoogle Scholar
6.Martineau, A., Indicatrices de croissance des fonctions de N variables—corrections et compléments, Inventiones Math. 3 (1967), 16–19.CrossRefGoogle Scholar
7.Martineau, A., Equations differentielles d'ordre infini, Bull. Soc. Math. France 95 (1967), 109–154.CrossRefGoogle Scholar
8.Treves, F., Linear partial differential equations with constant coefficients (New York, 1966).Google Scholar