A note on the zero-sequences of solutions of $f”+Af=0$
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- by Andreas Sauer PDF
- Proc. Amer. Math. Soc. 125 (1997), 1143-1147 Request permission
Abstract:
We give a sufficient condition for complex sequences to be zero-sequences of solutions of $f'' + Af=0$ where $A$ is transcendental entire and of finite order.References
- Steven B. Bank, A note on the zero-sequences of solutions of linear differential equations, Results Math. 13 (1988), no. 1-2, 1–11. MR 928136, DOI 10.1007/BF03323391
- Steven B. Bank and Ilpo Laine, On the oscillation theory of $f^{\prime \prime }+Af=0$ where $A$ is entire, Trans. Amer. Math. Soc. 273 (1982), no. 1, 351–363. MR 664047, DOI 10.1090/S0002-9947-1982-0664047-6
- Heinrich Behnke and Friedrich Sommer, Theorie der analytischen Funktionen einer komplexen Veränderlichen. , Die Grundlehren der mathematischen Wissenschaften, Band 77, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1962 (German). Zweite veränderte Auflage. MR 0147622, DOI 10.1007/978-3-662-01316-8
- Adolf Hurwitz, Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen, Die Grundlehren der mathematischen Wissenschaften, Band 3, Springer-Verlag, Berlin-New York, 1964 (German). Herausgegeben und ergänzt durch einen Abschnitt über geometrische Funktionentheorie von R. Courant. Mit einem Anhang von H. Röhrl; Vierte vermehrte und verbesserte Auflage. MR 0173749
- Ilpo Laine, Nevanlinna theory and complex differential equations, De Gruyter Studies in Mathematics, vol. 15, Walter de Gruyter & Co., Berlin, 1993. MR 1207139, DOI 10.1515/9783110863147
- Rolf Nevanlinna, Le théorème de Picard-Borel et la théorie des fonctions méromorphes, Chelsea Publishing Co., New York, 1974 (French). Reprinting of the 1929 original. MR 0417418
- Li-Chien Shen, Construction of a differential equation $y''+Ay=0$ with solutions having the prescribed zeros, Proc. Amer. Math. Soc. 95 (1985), no. 4, 544–546. MR 810160, DOI 10.1090/S0002-9939-1985-0810160-8
Additional Information
- Andreas Sauer
- Email: sauer@math.uni-duisberg.de
- Received by editor(s): October 11, 1995
- Additional Notes: This research was done during a visit at the University of Joensuu, Finland, financed by the DFG (Deutsche Forschungsgemeinschaft).
- Communicated by: Hal L. Smith
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1143-1147
- MSC (1991): Primary 34A20; Secondary 30D20
- DOI: https://doi.org/10.1090/S0002-9939-97-03819-7
- MathSciNet review: 1377005