arXiv subjects

M. A. Zemirni

Publications and source records attributed to M. A. Zemirni.

2 recordsLinked to original sources

arXiv2020

On the limits of real-valued functions in sets involving $ ψ$-density, and applications

We prove new results on upper and lower limits of real-valued functions by means of $ψ$-densities introduced by P. D. Barry in 1962. This allows us to improve several existing results on the growth of non-decreasing and unbounded real-valued functions in sets of positive density. The $ψ$-densities are also used to introduce a new concept of a limit for real-valued functions. The results in this paper are of interest in real analysis as well as in the theory of meromorphic functions.

math.CV↗

arXiv2020

On Petrenko's deviations and second order differential equations

New results on the oscillation of solutions of $f''+A(z)f=0$ and on the growth of solutions of $f''+A(z)f'+B(z)f=0$ are obtained, where $A$ and $B$ are entire functions. Petrenko's magnitudes of deviation of $g$ with respect to $\infty$ play a key rôle in the results, where $g$ represents one of the coefficients $A$ or $B$. These quantities are defined by $β^-(\infty,g) = \liminf_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$ and $β^+(\infty,g) = \limsup_{r\to\infty} \frac{\log M(r,g)}{T(r,g)}$.

math.CV↗