Related papers: On exponential type entire functions without zeros…

We study eigenfunctions of Schrodinger operators -y"+Py on the real line with zero boundary conditions, whose potentials P are real even polynomials with positive leading coefficients. For quartic potentials we prove that all zeros of all…

The main aim of this paper is twofold. First we generalize, in a novel way, most of the known non-vanishing results for the derivatives of the Riemann zeta function by establishing the existence of an infinite sequence of regions in the…

The paper deals with the determination of integral functional quality for control system of generalized linear dynamic object with exponential activation function by solving the inverse problem of dynamic programming. The obtained…

The paper determines all meromorphic functions with finitely many zeros in the plane having the property that a linear differential polynomial in the function, of order at least 3 and with rational functions as coefficients, also has…

Let $d \ge 1$, $p \ge d$, and let $\Omega$ be a smooth bounded open subset of $\mathbb{R}^d$. We prove some exponential integrability in the spirit of Moser-Trudinger's inequalities for measurable functions $u$ defined in $\Omega$ such that…

In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…

Exponentiable functors between quantaloid-enriched categories are characterized in elementary terms. The proof goes as follows: the elementary conditions on a given functor translate into existence statements for certain adjoints that obey…

This paper identifies necessary and sufficient conditions for the exactness of penalty functions in optimization problems whose constraint sets are not necessarily bounded. The case where the data of problems is locally Lipschitz,…

We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…

We prove an explicit integral formula for computing the product of two shifted Riemann zeta functions everywhere in the complex plane. We show that this formula implies the existence of infinite families of exact exponential sum identities…

Let $\mathcal{S}$ denote the family of all functions that are analytic and univalent in the unit disk $\mathbb{D}:=\{z: |z|<1\}$ and satisfy $f(0)=f^{\prime}(0)-1=0$. In the present paper, we consider certain subclasses of univalent…

The error term in the approximate functional equation for exponential sums involving the divisor function will be improved under certain conditions for the parameters of the approximate functional equation.

We prove, by topological methods, new results on the existence of nonzero positive weak solutions for a class of multi-parameter second order elliptic systems subject to functional boundary conditions. The setting is fairly general and…

The paper extends the widely used in optimisation theory decoupling techniques to infinite collections of functions. Extended concepts of uniform lower semicontinuity and firm uniform lower semicontinuity are discussed. The main theorems…

In the second part of this work was developed a technique of balayage of finite genus $q=0,1,2,\dots$ for measures (charges) and ($\delta$-) subharmonic functions of finite order to an arbitrary closed system of rays $S$ with vertex at…

We prove a strong form of model completenes for expansions of the field of real numbers by (the real and imaginary parts of) the modular function J, by the modular forms $E_4$ and $E_6$ and quasimodular form $E_2$ defined in the usual…

We characterize all linear operators which preserve spaces of entire functions whose zeros lie in a closed strip. Necessary and sufficient conditions are obtained for the related problem with real entire functions, and some classical…

For real-valued additive process $(X\_t)\_{t\geq 0}$ a recursive equation is derived for the entire positive moments of functionals $$I\_{s,t}= \int \_s^t\exp(-X\_u)du, \quad 0\leq s<t\leq\infty, $$ in case the Laplace exponent of $X\_t$…

In this article we review a new method for proving the nonexistence of positive solutions of elliptic inequalities in unbounded domains in $\rn$, which was recently introduced by the authors. We expose our method and new results on the two…

We utilize the same technique as in [arXiv:2205.04254 (2022)] to provide some representations of polynomials non-negative on a basic semi-algebraic set, defined by polynomial inequalities, under more general conditions. Based on each…