On The Eneström-Kakeya Theorem

نویسندگان

چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Eneström-Kakeya Theorem and Some of Its Generalizations

The study of the zeros of polynomials has a very rich history. In addition to having numerous applications, this study has been the inspiration for much theoretical research (including being the initial motivation for modern algebra). The earliest contributors to this subject were Gauss and Cauchy. Algebraic and analytic methods for finding zeros of a polynomial, in general, can be quite compli...

متن کامل

An EnestrÖm-Kakeya Theorem for Hermitian Polynomial Matrices

We extend the Eneström-Kakeya theorem and its refinement by Hurwitz to polynomial matrices H(z) with positive semidefinite coefficients. We determine an annular region containing the zeros of detH(z). A stability result for systems of linear difference equations is given as an application.

متن کامل

On a Kakeya-type Problem

Let A be a finite subset of an abelian group G . For every element bi of the sumset 2A={b0, b1, ..., b|2A|−1} we denote by Di={a − a′ : a, a′∈A; a+a′=bi} and ri=|{(a, a′) : a+a′=bi; a, a′∈A}| . After an eventual reordering of 2A , we may assume that r0>r1>...>r|2A|−1. For every 16s6|2A| we define Rs(A) = |D0∪D1∪...∪Ds−1| and Rs(k)= max{Rs(A) : A⊆G, |A|=k}. Bourgain and Katz and Tao obtained an ...

متن کامل

On Some Variants of the Kakeya Problem

Besicovitch and Rado [1] and Kinney [5] proved the following result: There is a closed set E ⊂ R2 with measure zero which contains a circle of every radius. The construction of Besicovitch and Rado works in Rd: If d ≥ 3 there is a closed set E ⊂ Rd with measure zero which contains a sphere of every radius. We will give an exposition of this construction in Section 1 below. One can ask whether a...

متن کامل