Related papers: On exponential type entire functions without zeros…

We present a new, short and independent proof of the Liouville-type theorem for entire and subharmonic functions of finite order bounded outside some set of zero planar density.

Abstract. In this work we derive a sufficient condition to ensure certain genus 0 entire function that can have only negative zeros. We also apply this result to the Riemann hypothesis and generalized Riemann hypothesis for some primitive…

For differential inequalities with the $\infty$-Laplacian in the principal part, we obtain conditions for the absence of solutions in unbounded domains. Examples are given to demonstrate the accuracy of these conditions.

We show that for any uniformly parabolic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term in the whole space or in any cylindrical smooth domain with smooth boundary data one can find an…

In this paper we have found a necessary and sufficient condition for equivalence of two norms on a linear space using the theory of exponential vector space. Exponential vector space is an ordered algebraic structure which can be considered…

We study infinite order differential operators acting in the spaces of exponential type entire functions. We derive conditions under which such operators preserve the set of Laguerre entire functions which consists of the polynomials…

We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.

Suppose that an almost periodic in Besicovitch's sense function $f(x)$ of several variables is the restriction to the real hyperplane of an entire function of exponential type $b$. Then its spectrum is contained in the ball of radius $b$…

We define and study analogues of exponentials for functions on noncommutative two-tori that depend on a choice of a complex structure. The major difference with the commutative case is that our noncommutative exponentials can be defined…

This paper studies a partial-fraction expansion for lossless negative imaginary systems and presents a generalized lossless negative imaginary lemma by allowing poles at zero. First, a necessary and sufficient condition for a system to be…

In this work we prove that an entire function $f(z)$ has only negative zeros if and only if its order is strictly less $1$, its root sequence is real-part dominating and there exists an nonnegative integer $m$ the real function…

This is a straightforward introduction to the properties of polynomials in many variables that do not vanish in the open upper half plane. Such polynomials generalize many of the well-known properties of polynomials with all real roots.

This article shows a very elementary and straightforward proof of the Implicit Function Theorem for differentiable maps $F(x,y)$ defined on a finite-dimensional Euclidean space. There are no hypothesis on the continuity of the partial…

The necessary and sufficient conditions for a function to be totally or partially separable are derived. It is shown that a function is totally separable if and only if each component of the gradient vector of depends only on the…

We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

We prove a form of the $\cos \pi \rho$ theorem which gives strong estimates for the minimum modulus of a transcendental entire function of order zero. We also prove a generalisation of a result of Hinkkanen that gives a sufficient condition…

We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.

$\tau$-Li coefficients describe if a function satisfies the Generalized Riemann Hypothesis or not. In this paper we prove that certain values of the $\tau$-Li coefficients lead to existence or non-existence of certain zeros. The first main…

We axiomatize a class of existentially closed exponential fields equipped with an $E$-derivation. We apply our results to the field of real numbers endowed with $exp(x)$ the classical exponential function defined by its power series…