共查询到20条相似文献,搜索用时 15 毫秒
1.
S. V. Tyshkevich 《Mathematical Notes》2007,81(5-6):851-853
2.
Do Yong Kwon 《Acta Mathematica Hungarica》2011,131(3):285-294
Let f(x)=a
d
x
d
+a
d−1
x
d−1+⋅⋅⋅+a
0∈ℝ[x] be a reciprocal polynomial of degree d. We prove that if the coefficient vector (a
d
,a
d−1,…,a
0) or (a
d−1,a
d−2,…,a
1) is close enough, in the l
1-distance, to the constant vector (b,b,…,b)∈ℝ
d+1 or ℝ
d−1, then all of its zeros have moduli 1. 相似文献
3.
DoYong Kwon 《Acta Mathematica Hungarica》2012,134(4):472-480
We derive sufficient conditions under which all but two zeros of reciprocal polynomials lie on the unit circle, and specify
the location of the remaining two zeros. 相似文献
4.
5.
Consider the polynomial equation
where 0 <r
1 ⪯ {irt}2⪯... ⪯r
n All zeros of this equation lie on the imaginary axis. In this paper, we show that no two of the zeros can be equal and the
gaps between the zeros in the upper half-plane strictly increase as one proceeds upward. Also we give some examples of geometric
progressions of the zeros in the upper half-plane in casesn = 6, 8, 10. 相似文献
6.
Leonid Golinski 《Acta Mathematica Hungarica》2002,96(3):169-186
Given a probability measure μ on the unit circle T, we study para-orthogonal polynomials Bn(.,w) (with fixed w ∈ T) and their zeros which are known to lie on the unit circle. We focus on the properties of zeros akin
to the well known properties of zeros of orthogonal polynomials on the real line, such as alternation, separation and asymptotic
distribution. We also estimate the distance between the consecutive zeros and examine the property of the support of μ to
attract zeros of para-orthogonal polynomials.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
7.
In this paper, we develop a rigorous algorithm for counting the real interval zeros of polynomials with perturbed coefficients that lie within a given interval, without computing the roots of any polynomials. The result generalizes Sturm’s Theorem for counting the roots of univariate polynomials to univariate interval polynomials. 相似文献
8.
We consider the zeros distributions of difference-differential polynomials which are the derivatives of difference products of entire functions.We also investigate the uniqueness problems of difference... 相似文献
9.
Barry Simon 《Journal of Mathematical Analysis and Applications》2007,329(1):376-382
We prove several results about zeros of paraorthogonal polynomials using the theory of rank one perturbations of unitary operators. In particular, we obtain new details on the interlacing of zeros for successive POPUC. 相似文献
10.
Mihai Stoiciu 《Journal of Approximation Theory》2006,139(1-2):29
The orthogonal polynomials on the unit circle are defined by the recurrence relation where for any k0. If we consider n complex numbers and , we can use the previous recurrence relation to define the monic polynomials Φ0,Φ1,…,Φn. The polynomial Φn(z)=Φn(z;α0,…,αn-2,αn-1) obtained in this way is called the paraorthogonal polynomial associated to the coefficients α0,α1,…,αn-1.We take α0,α1,…,αn-2 i.i.d. random variables distributed uniformly in a disk of radius r<1 and αn-1 another random variable independent of the previous ones and distributed uniformly on the unit circle. For any n we will consider the random paraorthogonal polynomial Φn(z)=Φn(z;α0,…,αn-2,αn-1). The zeros of Φn are n random points on the unit circle.We prove that for any the distribution of the zeros of Φn in intervals of size near eiθ is the same as the distribution of n independent random points uniformly distributed on the unit circle (i.e., Poisson). This means that, for large n, there is no local correlation between the zeros of the considered random paraorthogonal polynomials. 相似文献
11.
On zeros of polynomials orthogonal with respect to a quasi-definite inner product on the unit circle
In this paper we present some results concerning the zeros of sequences of polynomials orthogonal with respect to a quasi-definite inner product on the unit circle. We study zero general properties, the existence of sequences with prefixed zeros and some situations concerning the polynomials with multiple zeros. 相似文献
12.
V. A. Yudin 《Mathematical Notes》2007,82(3-4):564-568
In the space of continuous functions defined on the ball from ?n, n ≥ 2, we study the set of algebraic polynomials of least deviation from zero. Its width and dimension are estimated. 相似文献
13.
I. V. Belyakov 《Mathematical Notes》2006,80(3-4):339-344
For a wide class of symmetric trigonometric polynomials, the minimal deviation property is established. As a corollary, the extremal property is proved for the components of the Chebyshev polynomial mappings corresponding to symmetric algebras A α. 相似文献
14.
We give a new suffcient condition for all zeros of self-inversive polynomials to be on the unit circle, and find the location
of zeros. This generalizes some recent results of Lakatos [7], Schinzel [17], Lakatos and Losonczi [9], [10]. By this suffcient
condition the mentioned results can be treated in a unified way. 相似文献
15.
We prove that for any n×n matrix, A, and z with |z|A, we have that . We apply this result to the study of random orthogonal polynomials on the unit circle. 相似文献
16.
Arno B. J. Kuijlaars. 《Mathematics of Computation》1996,65(213):151-156
It is shown that the zeros of the Faber polynomials generated by a regular -star are located on the -star. This proves a recent conjecture of J. Bartolomeo and M. He. The proof uses the connection between zeros of Faber polynomials and Chebyshev quadrature formulas.
17.
Li-Chien Shen 《Proceedings of the American Mathematical Society》2001,129(3):873-879
Using the well-known fact that the Fourier transform is unitary, we obtain a class of orthogonal polynomials on the unit circle from the Fourier transform of the Laguerre polynomials (with suitable weights attached). Some related extremal problems which arise naturally in this setting are investigated.
18.
In this paper we extend a classical result due to Cauchy and its improvement due to Datt and Govil to a class of lacunary
type polynomials. 相似文献
19.
Conditions are presented for the identification of (directed) arcs for the traveling salesman problem, that can be eliminated with at least one optimal solution remaining. The conditions are not based on lower or upper bounds; the presence of an identified arc in a solution implies that the solution is not 3-optimal. An example illustrates how to use the conditions. 相似文献
20.
W.M.Shah A.Liman 《分析论及其应用》2004,20(1):16-27
Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem. 相似文献