JournalsprimsVol. 30, No. 5pp. 745–765

Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order

  • Carlos A. Berenstein

    University of Maryland, College Park, USA
  • Roger Gay

    Université de Bordeaux I, Talence, France
  • Alekos Vidras

    University of Cyprus, Nicosia, Cyprus
Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order cover

Abstract

It is shown that every entire function f ∈ Exp0(Cn), f(0) ≠ 0 is "slowly decreasing". As an application of this property, a theorem on analytic continuation of solutions of infinite order differential equations with constant coefficients is proven.

Cite this article

Carlos A. Berenstein, Roger Gay, Alekos Vidras, Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order. Publ. Res. Inst. Math. Sci. 30 (1994), no. 5, pp. 745–765

DOI 10.2977/PRIMS/1195165583