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Zero distribution of solutions of complex linear differential equations determines growth of coefficients

✍ Scribed by Janne Heittokangas; Jouni Rättyä

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
121 KB
Volume
284
Category
Article
ISSN
0025-584X

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✦ Synopsis

It is shown that the exponent of convergence λ(f ) of any solution f of

In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim's 1969 representation of coefficients in terms of ratios of linearly independent solutions.

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✍ T. A. Burton; P. W. Eloe; M. N. Islam 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 359 KB 👁 1 views

## Abstract Using a degree‐theoretic result of Granas, a homotopy is constructed enabling us to show that if there is an __a priori__ bound on all possible __T__‐periodic solutions of a Volterra equation, then there is a __T__‐periodic solution. The __a priori__ bound is established by means of a L