Related papers: Monotonous period function for equivariant differe…
For an indeterminate moment problem we denote the orthonormal polynomials by P_n. We study the relation between the growth of the function P(z)=(\sum_{n=0}^\infty|P_n(z)|^2)^{1/2} and summability properties of the sequence (P_n(z)). Under…
For a sequence of continuous, monotone functions $f_1,\dots,f_n \colon I \to \mathbb{R}$ ($I$ is an interval) we define the mapping $M \colon I^n \to I^n$ as a Cartesian product of quasi-arithmetic means generated by $f_j$-s. It is known…
We prove that all zeros of the polynomials orthogonal with respect to a measure $d \mu(x;a) = d \mu(x) + M \delta(x-a)$, where $d\mu$ is a nonatomic positive Borel measure and $M>0$, are increasing functions of the mass point $a$. Thus we…
The classical model of q-damped oscillator is introduced and solved in terms of Jackson q-exponential function for three different cases, under-damped, over-damped and the critical one. It is shown that in all three cases solution is…
An integrable discretization of the inhomogeneous Ablowitz-Ladik model with a linear force is introduced. Conditions on parameters of the discretization which are necessary for reproducing Bloch oscillations are obtained. In particular, it…
Let $\mu(n)$ be the M\"obius function, $e(z) = \exp(2\pi iz)$, $x$ real and $2\leq y \leq x$. This paper proves two sequences $(\mu(n))$ and $(e(n^k \alpha))$ are strongly orthogonal in short intervals. That is, if $k \geq 3$ being fixed…
We describe a time-dependent functional involving the relative entropy and the $\dot{H}^1$ seminorm, which decreases along solutions to the spatially homogeneous Landau equation with Coulomb potential. The study of this monotone functionial…
We study the monotonic behaviour of the zeros of the multiple Jacobi-Angelesco orthogonal polynomials, in the diagonal case, with respect to the parameters $\alpha,\beta$ and $\gamma$. We prove that the zeros are monotonic functions of…
We study the behaviour of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent e.g. the elastic or electromagnetic response of a two-component…
The discrete acyclic convolution computes the 2n-1 sums sum_{i+j=k; (i,j) in [0,1,2,...,n-1]^2} (a_i b_j) in O(n log n) time. By using suitable offsets and setting some of the variables to zero, this method provides a tool to calculate all…
We consider the problem of finding the shortest possible period for an exactly periodic solution to some given autonomous ordinary differential equation. We show that, given a pair of Lyapunov-like observable functions defined over the…
If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of $n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$ ($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference equation…
We investigate the topological zeta function for unimodal maps in general and dynamical zeta functions for the tent map in particular. For the generic situation, when the kneading sequence is aperiodic, it is shown that the zeta functions…
This is the continuation of previous article. For subspaces $M^n(t)$ and $M^{n-m}(t)$ which are invariant manifolds of the differential equation under consideration we build a change of variables which splits this equation into a system of…
We consider the "moment vanishing problem" for a general class of piecewise-analytic functions which satisfy on each continuity interval a linear ODE with polynomial coefficients. This problem, which essentially asks how many zero first…
In this paper we continue work in the direction of a characterization of rational period functions on the Hecke groups. We examine the role that Hecke-symmetry of poles plays in this setting, and pay particular attention to non-symmetric…
We establish some new Tur\'an's type inequalities for orthogonal polynomials defined by a three-term recurrence with monotonic coefficients. As a corollary we deduce asymptotic bounds on the extreme zeros of orthogonal polynomials with…
A monotonicity property of Harnack inequality is proved for positive invariant harmonic functions in the unit ball.
This paper concerns the inverse source problem for the time-harmonic wave equation in a one dimensional domain. The goal is to determine the source function from the boundary measurements. The problem is challenging due to complexity of the…
In this paper, we consider the value distribution of the differential polynomials $f^2f^{(k)}-1$ where $k$ is a positive integer, and obtain some estimates only by the reduced counting function. Our result answers a question in (Some…