Speaker
Description
The classes of standard functions introduced by B.N. Khabibullin are considered. The concept of a model function of growth covers a large class of functions. Functions $f$ of finite order with respect to the model function can have an order of growth in the classical sense equal to infinity or zero. For example, the model functions of growth include functions of $r>0$ of the form $\exp^{\circ n}r$, where $\exp^{\circ n}$ is the $n$-th superposition with $n=1,2,\dots$ of the exponential function $\exp$, degree of the logarithmic function $\ln^p(e+r)$ for any $p\geq 1$, and in general any differentiable function $M(r)>0$ such that the function $rM'(r)>0$ increases for $r>0$. We prove that for any function $f$ defined on $\mathbb{R}^+$ whose growth is determined by a model function of growth $M$, there exist its own proximate growth functions with respect to the model growth function $M$ that estimate $f$ above and below. Thus, we solve the extended Hadamard problem for a fairly wide class of entire and subharmonic functions. The proof is constructive.
The research is supported by Russian Science Foundation (project No. 22-21-00012).
