共查询到20条相似文献,搜索用时 31 毫秒
1.
S. B. Damelin 《Monatshefte für Mathematik》2003,138(2):111-131
For a real interval I of positive length, we prove a necessary and sufficient condition which ensures that the continuous L
p
(0 < p ⩽ ∞) norm of a weighted polynomial, P
n
w
n
, deg P
n
⩽ n, n ⩾ 1 is in an nth root sense, controlled by its corresponding discrete H?lder norm on a very general class of discrete subsets of I. As a by product of our main result, we establish inequalities and theorems dealing with zero distribution, zero location and sup and L
p
infinite–finite range inequalities.
Received April 4, 2001; in final form June 21, 2002 相似文献
2.
We study asymptotics for orthogonal polynomials and other extremalpolynomials on infinite discrete sets, typical examples beingthe Meixner polynomials and the Charlier polynomials. Followingideas of Rakhmanov, Dragnev and Saff, weshow that the asymptoticbehaviour is governed by a constrained extremal energy problemfor logarithmic potentials, which can be solved explicitly.We give formulas for the contracted zero distributions, thenth root asymptotics and the asymptotics of the largest zeros.1991 Mathematics Subject Classification: 42C05, 33C25, 31A15. 相似文献
3.
Vilmos Totik 《Potential Analysis》2014,40(4):511-524
In connection with a problem of H. Widom it is shown that if a compact set K on the complex plane contains a smooth Jordan arc on its outer boundary, then the minimal norm of monic polynomials of degree n?=?1,2,... is at least (1?+?β)cap(K) n with some β?>?0, where cap(K) n would be the theoretical lower bound. It is also shown that the rate (1?+?o(1))cap(K) n is possible only for compact for which the unbounded component of the complement is simply connected. A related result for sets lying on the real line is also proven. 相似文献
4.
We extend results by Barnsley et al. about orthogonal polynomials on Julia sets to the case of generalized Julia sets. The equilibrium measure is considered. In addition, we discuss optimal smoothness of Green’s functions and Parreau–Widom criterion for a special family of real generalized Julia sets. 相似文献
5.
This paper addresses Gabor analysis on a discrete periodic set. Such a scenario can potentially find its applications in signal processing where signals may present on a union of disconnected discrete index sets. We focus on the Gabor systems generated by characteristic functions. A sufficient and necessary condition for a set to be a tight Gabor set in discrete periodic sets is obtained; discrete periodic sets admitting a tight Gabor set are also characterized; the perturbation of tight Gabor sets is investigated; an algorithm to determine whether a set is a tight Gabor set is presented. Furthermore, we prove that an arbitrary Gabor frame set can be represented as the union of a tight Gabor set and a Gabor Bessel set. 相似文献
6.
Helton J. William Klep Igor McCullough Scott Volčič Jurij 《Foundations of Computational Mathematics》2021,21(2):575-611
Foundations of Computational Mathematics - The free closed semialgebraic set $${\mathcal {D}}_f$$ determined by a hermitian noncommutative polynomial $$f\in {\text {M}}_{{\delta }}({\mathbb... 相似文献
7.
Christiansen Jacob Stordal Henriksen Christian Pedersen Henrik Laurberg Petersen Carsten Lunde 《Potential Analysis》2019,50(3):401-413
Potential Analysis - For a probability measure with compact and non-polar support in the complex plane we relate dynamical properties of the associated sequence of orthogonal polynomials {Pn} to... 相似文献
8.
《复变函数与椭圆型方程》2012,57(11):1003-1014
This paper studies the effectiveness of another kind of transposed sets of polynomials of one complex variable in closed regions, open discs, at the origin and for all entire functions. In addition, an upper bound for the order of these sets in this case is obtained. 相似文献
9.
10.
A. I. Aptekarev J. S. Dehesa A. Martínez-Finkelshtein R. Yáñez 《Constructive Approximation》2009,30(1):93-119
Given a nontrivial Borel measure on ℝ, let p
n
be the corresponding orthonormal polynomial of degree n whose zeros are λ
j
(n), j=1,…,n. Then for each j=1,…,n,
with
defines a discrete probability distribution. The Shannon entropy of the sequence {p
n
} is consequently defined as
In the case of Chebyshev polynomials of the first and second kinds, an explicit and closed formula for
is obtained, revealing interesting connections with number theory. In addition, several results of numerical computations
exemplifying the behavior of
for other families are presented.
相似文献
11.
12.
In this paper, it is shown that certain classes of regular functions of several complex variables be represented by exponential sets of polynomials in hyperelliptical regions. Moreover, an upper bound for the order of exponential set is given. 相似文献
13.
14.
The discrete Chebyshev polynomials are orthogonal with respect to a distribution, which is a step function with jumps one unit at the points , N being a fixed positive integer. By using a double integral representation, we have recently obtained asymptotic expansions for in the double scaling limit, namely, and , where and ; see [8]. In this paper, we continue to investigate the behavior of these polynomials when the parameter b approaches the endpoints of the interval (0, 1). While the case is relatively simple (because it is very much like the case when b is fixed), the case is quite complicated. The discussion of the latter case is divided into several subcases, depending on the quantities n, x, and , and different special functions have been used as approximants, including Airy, Bessel, and Kummer functions. 相似文献
15.
Murota et al. have recently developed a theory of discrete convex analysis as a framework to solve combinatorial optimization problems using ideas from continuous optimization. This theory concerns M-convex functions on jump systems. We introduce here a family of M-concave functions arising naturally from polynomials (over the field of Puiseux series) with prescribed non-vanishing properties. We also provide a short proof of Speyer's “hive theorem” which he used to give a new proof of Horn's conjecture on eigenvalues of sums of Hermitian matrices. Due to limited space a more coherent treatment and proofs will appear elsewhere. 相似文献
16.
In this paper we present an algorithm for recursively generating orthogonal bivariate polynomials on a discrete set S 2. For this purpose we employ commuting pairs of real symmetric matrices H, K
n×n
to obtain, in a certain sense, a two dimensional Hermitian Lanczos method. The resulting algorithm relies on a recurrence having a slowly growing length. Practical implementation issues an applications are considered. The method can be generalized to compute orthogonal polynomials depending on an arbitrary number of variables. 相似文献
17.
We characterize distributions with respect to which the membersof a Tchebychev set of polynomials are orthogonal when theysatisfy differential equations with polynomial coefficients.As an application, we find a real weight of bounded variationwith support in [0, ) for Bessel polynomials. 相似文献
18.
Let f be a polynomial of degree at least two. We shall showthat the Julia set J(f) of f is uniformly perfect. This meansthat there is a constant c(0,1) depending on f only such thatwhenever zJ(f) and 0 < r < diam J(f) then J(f) intersectsthe annulus {w:cr |w z| r}. 相似文献
19.
《复变函数与椭圆型方程》2012,57(5):383-391
In this paper, some geometric properties of connected Julia sets and filled-in Julia sets of polynomials are given. 相似文献
20.
最近,Dillon和Dobbertin证明了在有限域Fq(q=2m)的乘法群中,多项式(x+1)d+xd+1(其中d=22k-2k+1)的像集是一个新的具有Singer参数的循环差集.利用有限域上的Fourier分析,本文证明了在有限域Fq(q=2m)的乘法群中,一些用Dickson多项式构造的集合是具有Singer参数的循环差集. 相似文献