Related papers: On Certain Bounds for Genus 0 Entire Functions

Given l<s<m an upper bound on the s norm is given using l norm and m norm. The result is applied in bounding odd values of zeta function, binomial sums and gamma and beta functions.

Using tools provided by the theory of abstract convexity, we extend conditions for zero duality gap to the context of nonconvex and nonsmooth optimization. Mimicking the classical setting, an abstract convex function is the upper envelope…

We prove that convex functions of finite order on the real line and subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some set of zero relative Lebesgue density, are bounded from above…

The paper studies entire functions of finite order of growth for which a representation of the form $\psi(z) = 1+ O(|z|^{-\mu}), \mu >0,$ as $z\to \infty$, is valid on a fixed ray of the complex plane. The main result is the following.…

We present a rational extension of Newton diagram for the positivity of ${}_1F_2$ generalized hypergeometric functions. As an application, we give upper and lower bounds for the transcendental roots $\beta(\alpha)$ of \begin{align*}…

We determine upper and lower bounds on the zero forcing number of 2-connected outerplanar graphs in terms of the structure of the weak dual. We show that the upper bound is always at most half the number of vertices of the graph. This work…

We study zeroes of Gaussian analytic functions in a strip in the complex plane, with translation-invariant distribution. We prove that the a limiting horizontal mean counting-measure of the zeroes exists almost surely, and that it is…

A monotone iterative method is proposed to solve nonlinear discrete boundary value problems with the support of upper and lower solutions. We establish some new existence results. Under some sufficient conditions, we establish maximum…

We prove that the Fourier dimension of any Boolean function with Fourier sparsity $s$ is at most $O\left(s^{2/3}\right)$. Our proof method yields an improved bound of $\widetilde{O}(\sqrt{s})$ assuming a conjecture of…

In this paper we answer a question raised in [25], Sec. 4, by showing that the genus zero moduli operad $\{\bar{M}_{0,n+1}\}$ can be endowed with natural descent data that allow it to be considered as the lift to ${\rm Spec}\,\Z$ of an…

We show that there exist unbounded functionals on the spaces of sequences that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint.

In Boundary Element Method, Green's function with no boundary conditions is used for solving Laplace's equation with Dirichlet boundary condition. To determine the gradient of solution on the boundary, we need to solve the boundary integral…

In the setup of i.i.d.~observations and a real valued differentiable functional~$T$, locally asymptotic upper bounds are derived for the power of one-sided tests (simple, versus large values of~$T$)and for the confidence probability of…

In this paper we consider a class of boundary value problems for third order nonlinear functional differential equation. By the reduction of the problem to operator equation we establish the existence and uniqueness of solution and…

Let $Z$ and $W$ be a pair of point distributions of finite upper density on the complex plane $\mathbb C$ with the real axis $\mathbb R$. We give several variants of necessary and at the same time sufficient conditions for their…

The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in…

Let $A(s) = \sum_n a_n n^{-s}$ be a Dirichlet series admitting meromorphic continuation to the complex plane. Assume we know the location of the poles of $A(s)$ with $|\Im s| \leq T$, and their residues, for some large constant $T$. It is…

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over M_g, specifically, the…

We derive a lower and an upper bound for the rank of the finite part of operator $K$-theory groups of maximal and reduced $C^*$-algebras of finitely generated groups. The lower bound is based on the amount of polynomially growing conjugacy…

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…