arXiv subjects
Publications and source records attributed to Alexander I. Kheyfits.
An elementary, at the undergraduate level derivation is given of precise upper bounds of the number of various RNA secondary structures. The method works when the generating function has multiple singularities at the circle of convergence, nor does the method require the Taylor coefficients to be positive. Examples from the current research literature are considered.
The Valiron-Titchmarsh theorem on asymptotic behavior of entire functions with negative zeros is extended to subharmonic functions in $\mathbb{R}^n, n\geq 3$. We also show that the existence of the limit $\lim_{\rti} \frac{\log u(r)}{N(r)}$, where $N(r)$ is the averaged counting function of a subharmonic function $u$ with the associated masses on a ray implies the regular asymptotic behavior separately for $u$ and for $N$.
Subharmonic functions associated with the stationary Schrodinger operator are its weak subsolutions under appropriate assumptions on the potential of the operator. We prove for these functions analogs of several classical results on analytic and subharmonic functions, such as the Phragmen-Lindelof theorem with the precise growth rate, the Blaschke theorem on bounded analytic functions, the Carleman formula, the Hayman-Azarin theorem on asymptotic behavior of special subharmonic functions in many-dimensional cones.