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Displaying 1841 –
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Combining the study of the simple random walk on graphs, generating functions (especially
Green functions), complex dynamics and general complex analysis we introduce a new method
for spectral analysis on self-similar graphs.First, for a rather general,
axiomatically defined class of self-similar graphs a graph theoretic analogue to the
Banach fixed point theorem is proved. The subsequent results hold for a subclass
consisting of “symmetrically” self-similar graphs which however is still more general
then...
We investigate the growth and fixed points of meromorphic solutions of higher order linear differential equations with meromorphic coefficients and their derivatives. Our results extend the previous results due to Peng and Chen.
We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.
We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.
If p(z) be a polynomial of degree n, which does not vanish in |z| < k, k < 1, then it was conjectured by Aziz [Bull. Austral. Math. Soc. 35 (1987), 245-256] that [...] In this paper, we consider the case k < r < 1 and present a generalization as well as improvement of the above inequality.
The main purpose of this paper is to partly answer a question of L. Z. Yang [Israel J. Math. 147 (2005), 359-370] by proving that every entire solution f of the differential equation has infinite order and its hyperorder is a positive integer or infinity, where P is a nonconstant entire function of order less than 1/2. As an application, we obtain a uniqueness theorem for entire functions related to a conjecture of Brück [Results Math. 30 (1996), 21-24].
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