An unsolvable Cousin problem

Author:

Rubel Lee A.

Abstract

We construct a Laurent series n = A n z n \sum \nolimits _{n = - \infty }^\infty {{A_n}{z^n}} , convergent in an annulus { ρ > | z | > 1 / ρ } \left \{ {\rho > \left | z \right | > 1/\rho } \right \} for some ρ > 1 \rho > 1 , which satisfies an algebraic differential equation (ADE) there, but such that neither of the series n = 0 A n z n \sum \nolimits _{n = 0}^\infty {{A_n}{z^n}} and n = 1 A n z n \sum \nolimits _{n = - \infty }^{ - 1} {{A_n}{z^n}} satisfies any ADE.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference11 articles.

1. On the hypertranscendence of meromorphic solutions of certain functional equations;Bank, Steven B.;Proc. Roy. Soc. Edinburgh Sect. A,1979

2. Coherent families of polynomials;Boshernitzan, Michael;Analysis,1986

3. A differentially algebraic replacement theorem, and analog computability;Lipshitz, Leonard;Proc. Amer. Math. Soc.,1987

4. Über Dirichletsche Reihen und algebraische Differentialgleichungen;Ostrowski, Alexander;Math. Z.,1920

5. G. Pólya, Über das Anwachsen von ganzen Funktionen die einer Differentialgleichung genügen, Vierteljahrschrift Naturforsch. Gesellschaft Zürich 61 (1916), 531-545.

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