ISSN:
1420-8903
Keywords:
Keywords. Complex functional equations, meromorphic solutions, Nevanlinna theory.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Summary. We consider meromorphic solutions in the complex plane to functional equations of the form $ \ssize\sum_{j=0}^na_j(z)f(c^jz) =Q(z) $ , where 0 〈 |c| 〈 1, $ n \in {\Bbb N} $ and $ a_0,\ldots ,a_n,Q $ are meromorphic functions. If the coefficients $ a_0,\ldots ,a_n $ are constants and $ \ssize\sum_{j=0}^na_jc^{jk}\neq 0 $ for all $ k \in {\Bbb Z} $ , then exactly one meromorphic solution exists. In the general case, we give growth estimates for the solutions f as well as for the exponent of convergence $ \lambda (1/f) $ of poles and $ \lambda (f) $ of zeros of f. Similar results hold in the case 1 〈 |c| 〈 + $ \infty $ . Concluding remarks show that the case |c| = 1 is different.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000100050143
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