当前期刊: Constructive Approximation Go to current issue    加入关注   
显示样式:        排序: IF: - GO 导出
我的关注
我的收藏
您暂时未登录!
登录
  • Turán-Type Reverse Markov Inequalities for Polynomials with Restricted Zeros
    Constr. Approx. (IF 1.146) Pub Date : 2020-06-05
    Tamás Erdélyi

    Let \(\mathcal{P}_n^c\) denote the set of all algebraic polynomials of degree at most n with complex coefficients. Let $$\begin{aligned} D^+ := \{z \in \mathbb {C}: |z| \le 1, \text { Im}(z) \ge 0\}\,. \end{aligned}$$ For integers \(0 \le k \le n\) let \(\mathcal{F}_{n,k}^c\) be the set of all polynomials \(P \in \mathcal{P}_n^c\) having at least \(n-k\) zeros in \(D^+\). Let $$\begin{aligned} \Vert

    更新日期:2020-06-05
  • Boundary Behavior of Optimal Polynomial Approximants
    Constr. Approx. (IF 1.146) Pub Date : 2020-05-21
    Catherine Bénéteau, Myrto Manolaki, Daniel Seco

    In this paper, we provide an efficient method for computing the Taylor coefficients of \(1-p_n f\), where \(p_n\) denotes the optimal polynomial approximant of degree n to 1/f in a Hilbert space \(H^2_\omega \) of analytic functions over the unit disc \(\mathbb {D}\), and f is a polynomial of degree d with d simple zeros. As a consequence, we show that in many of the spaces \(H^2_\omega \), the sequence

    更新日期:2020-05-21
  • Rational Minimax Iterations for Computing the Matrix p th Root
    Constr. Approx. (IF 1.146) Pub Date : 2020-05-12
    Evan S. Gawlik

    In a previous paper by the author, a family of iterations for computing the matrix square root was constructed by exploiting a recursion obeyed by Zolotarev’s rational minimax approximants of the function \(z^{1/2}\). The present paper generalizes this construction by deriving rational minimax iterations for the matrix pth root, where \(p \ge 2\) is an integer. The analysis of these iterations is considerably

    更新日期:2020-05-12
  • Hermite-Poulain Theorems for Linear Finite Difference Operators
    Constr. Approx. (IF 1.146) Pub Date : 2020-05-12
    Olga Katkova, Mikhail Tyaglov, Anna Vishnyakova

    We establish analogues of the Hermite-Poulain theorem for linear finite difference operators with constant coefficients defined on sets of polynomials with roots on a straight line, in a strip, or in a half-plane. We also consider the central finite difference operator of the form $$\begin{aligned} \Delta _{\theta , h}(f)(z)=e^{i\theta }f(z+ih)-e^{-i\theta }f(z-ih), \quad \theta \in [0,\pi ),\ \ h\in

    更新日期:2020-05-12
  • Approximation to uniform distribution in $$\mathrm {SO}(3)$$SO(3)
    Constr. Approx. (IF 1.146) Pub Date : 2020-05-09
    Carlos Beltrán, Damir Ferizović

    Using the theory of determinantal point processes we give upper bounds for the Green and Riesz energies for the rotation group \(\mathrm {SO}(3)\), with Riesz parameter up to 3. The Green function is computed explicitly, and a lower bound for the Green energy is established, enabling comparison of uniform point constructions on \(\mathrm {SO}(3)\). The variance of rotation matrices sampled by a certain

    更新日期:2020-05-09
  • On a Uniqueness Theorem of E. B. Vul
    Constr. Approx. (IF 1.146) Pub Date : 2020-04-27
    Sasha Sodin

    We recall a uniqueness theorem of E. B. Vul pertaining to a version of the cosine transform originating in spectral theory. Then we point out an application to the Bernstein approximation problem with non-symmetric weights: a theorem of Volberg is proved by elementary means.

    更新日期:2020-04-27
  • Planar Sampling Sets for the Short-Time Fourier Transform
    Constr. Approx. (IF 1.146) Pub Date : 2020-04-09
    Philippe Jaming, Michael Speckbacher

    This paper considers the problem of restricting the short-time Fourier transform to sets of nonzero measure in the plane. Thereby, we study under which conditions one has a sampling set and provide estimates of the corresponding sampling bound. In particular, we give a quantitative estimate for the lower sampling bound in the case of Hermite windows and derive a sufficient condition for a large class

    更新日期:2020-04-18
  • Fejér Polynomials and Control of Nonlinear Discrete Systems
    Constr. Approx. (IF 1.146) Pub Date : 2019-06-25
    D. Dmitrishin, P. Hagelstein, A. Khamitova, A. Korenovskyi, A. Stokolos

    We consider optimization problems associated with a delayed feedback control (DFC) mechanism for stabilizing cycles of one-dimensional discrete time systems. In particular, we consider a delayed feedback control for stabilizing T-cycles of a differentiable function \(f: \mathbb {R}\rightarrow \mathbb {R}\) of the form $$\begin{aligned} x(k+1) = f(x(k)) + u(k), \end{aligned}$$ where $$\begin{aligned}

    更新日期:2020-04-18
  • Menshov Type Correction Theorems for Sequences of Compact Operators
    Constr. Approx. (IF 1.146) Pub Date : 2019-03-28
    Grigori A. Karagulyan

    We prove Menshov type “correction” theorems for sequences of compact operators, recovering several results of Fourier series in trigonometric and Walsh systems. The paper clarifies the main ingredient that is important in the study of such “correction” theorems. That is the weak-\(L^1\) estimate for the maximal Fourier sums of indicator functions of some specific sets.

    更新日期:2020-04-18
  • An Extension of Laplace’s Method
    Constr. Approx. (IF 1.146) Pub Date : 2018-08-17
    Gergő Nemes

    Asymptotic expansions are obtained for contour integrals of the form $$\begin{aligned} \int _a^b \exp \left( - zp(t) + z^{\nu /\mu } r(t) \right) q(t)\mathrm{d}t, \end{aligned}$$ in which z is a large real or complex parameter; p(t), q(t), and r(t) are analytic functions of t; and the positive constants \(\mu \) and \(\nu \) are related to the local behavior of the functions p(t) and r(t) near the

    更新日期:2020-04-18
  • Jacobi–Angelesco Multiple Orthogonal Polynomials on an r -Star
    Constr. Approx. (IF 1.146) Pub Date : 2019-03-07
    Marjolein Leurs, Walter Van Assche

    We investigate type I multiple orthogonal polynomials on r intervals that have a common point at the origin and endpoints at the r roots of unity \(\omega ^j\), \(j=0,1,\ldots ,r-1\), with \(\omega = \exp (2\pi i/r)\). We use the weight function \(|x|^\beta (1-x^r)^\alpha \), with \(\alpha ,\beta >-1\), for the multiple orthogonality relations. We give explicit formulas for the type I multiple orthogonal

    更新日期:2020-04-18
  • Sharp Approximations for the Ramanujan Constant
    Constr. Approx. (IF 1.146) Pub Date : 2019-05-17
    Song-Liang Qiu, Xiao-Yan Ma, Ti-Ren Huang

    In this paper, the authors present sharp approximations in terms of sine function and polynomials for the so-called Ramanujan constant (or the Ramanujan R-function) R(a), by showing some monotonicity, concavity and convexity properties of certain combinations defined in terms of R(a), \(\sin (\pi a)\) and polynomials. Some properties of the Riemann zeta function and its related special sums are presented

    更新日期:2020-04-18
  • Bounds for $$L_p$$Lp -Discrepancies of Point Distributions in Compact Metric Measure Spaces
    Constr. Approx. (IF 1.146) Pub Date : 2019-07-01
    M. M. Skriganov

    Upper bounds for the \(L_p\)-discrepancies of point distributions in compact metric measure spaces are proved for all exponents \(0

    更新日期:2020-04-18
  • Szegő Condition and Scattering for One-Dimensional Dirac Operators
    Constr. Approx. (IF 1.146) Pub Date : 2018-10-19
    R. V. Bessonov

    We prove the existence of modified wave operators for one-dimensional Dirac operators whose spectral measures belong to the Szegő class on the real line.

    更新日期:2020-04-18
  • Ambient Approximation on Embedded Submanifolds
    Constr. Approx. (IF 1.146) Pub Date : 2020-03-09
    L.-B. Maier

    In this paper, we present a generalization of Lehmann’s approach for solving approximation problems on hypersurfaces to situations with arbitrary codimension. We show that as in the case of hypersurfaces, the method is able to transfer approximation orders from the ambient space to the submanifold. In particular, the resulting approximant is \({\mathrm {C}}^{m-2}\) and the error decays at an optimal

    更新日期:2020-04-18
  • The Generalized Operator Based Prony Method
    Constr. Approx. (IF 1.146) Pub Date : 2020-02-27
    Kilian Stampfer, Gerlind Plonka

    The generalized Prony method is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator A. However, this procedure requires the evaluation of higher powers of the linear operator A that are often expensive to provide. In this paper we propose two important extensions of the generalized Prony method

    更新日期:2020-04-18
  • Scaling Limits of Jacobi Matrices and the Christoffel–Darboux Kernel
    Constr. Approx. (IF 1.146) Pub Date : 2020-02-20
    Jonathan Breuer

    We study scaling limits of deterministic Jacobi matrices, centered around a fixed point \(x_0\), and their connection to the scaling limits of the Christoffel–Darboux kernel at that point. We show that in the case when the orthogonal polynomials are bounded at \(x_0\), a subsequential limit always exists and can be expressed as a canonical system. We further show that under weak conditions on the associated

    更新日期:2020-04-18
  • Five Point Energy Minimization: A Synopsis
    Constr. Approx. (IF 1.146) Pub Date : 2020-02-13
    Richard Evan Schwartz

    This paper is a condensation of my arXiv monograph entitled Schwartz “The phase transition in 5 point energy minimization”, 2016. arXiv:1610.03303, which contains a complete proof that there is a constant such that the triangular bi-pyramid is the minimizer, amongst all 5 point configurations on the sphere, with respect to the power law potential \(R_s(r)=\mathrm{sign}(s)/r^s\), if and only if . In

    更新日期:2020-04-18
  • Sharp Results on Sampling with Derivatives in Shift-Invariant Spaces and Multi-Window Gabor Frames
    Constr. Approx. (IF 1.146) Pub Date : 2019-03-11
    Karlheinz Gröchenig, José Luis Romero, Joachim Stöckler

    We study the problem of sampling with derivatives in shift-invariant spaces generated by totally-positive functions of Gaussian type or by the hyperbolic secant. We provide sharp conditions in terms of weighted Beurling densities. As a by-product we derive new results about multi-window Gabor frames with respect to vectors of Hermite functions or totally positive functions.

    更新日期:2020-04-18
  • Rational Solutions of the Painlevé-III Equation: Large Parameter Asymptotics
    Constr. Approx. (IF 1.146) Pub Date : 2019-05-29
    Thomas Bothner, Peter D. Miller

    The Painlevé-III equation with parameters \(\Theta _0=n+m\) and \(\Theta _\infty =m-n+1\) has a unique rational solution \(u(x)=u_n(x;m)\) with \(u_n(\infty ;m)=1\) whenever \(n\in \mathbb {Z}\). Using a Riemann–Hilbert representation proposed in Bothner et al. (Stud Appl Math 141:626–679, 2018), we study the asymptotic behavior of \(u_n(x;m)\) in the limit \(n\rightarrow +\infty \) with \(m\in \mathbb

    更新日期:2020-04-18
  • Weighted Norm Inequalities for Fractional Bergman Operators
    Constr. Approx. (IF 1.146) Pub Date : 2019-06-25
    Benoît F. Sehba

    We prove in this paper one weight norm inequalities for some positive Bergman-type operators.

    更新日期:2020-04-18
  • Quadrature Points via Heat Kernel Repulsion
    Constr. Approx. (IF 1.146) Pub Date : 2019-07-11
    Jianfeng Lu, Matthias Sachs, Stefan Steinerberger

    We discuss the classical problem of how to pick N weighted points on a d-dimensional manifold so as to obtain a reasonable quadrature rule $$\begin{aligned} \frac{1}{|M|}\int _{M}{f(x) \mathrm{d}x} \simeq \sum _{n=1}^{N}{a_i f(x_i)}. \end{aligned}$$ This problem, naturally, has a long history; the purpose of our paper is to propose selecting points and weights so as to minimize the energy functional

    更新日期:2020-04-18
  • Rational Extension of the Newton Diagram for the Positivity of $${}_1F_2$$1F2 Hypergeometric Functions and Askey–Szegö Problem
    Constr. Approx. (IF 1.146) Pub Date : 2019-05-03
    Yong-Kum Cho, Seok-Young Chung, Hera Yun

    We present a rational extension of the 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 $$\begin{aligned} \int _0^{j_{\alpha , 2}} t^{-\beta } J_\alpha (t) \hbox {d}t = 0\qquad (-\,1<\alpha \le 1/2), \end{aligned}$$ where \(j_{\alpha , 2}\) denotes the second positive

    更新日期:2020-04-18
  • Gaussian Bounds for the Weighted Heat Kernels on the Interval, Ball, and Simplex
    Constr. Approx. (IF 1.146) Pub Date : 2019-03-18
    Gerard Kerkyacharian, Pencho Petrushev, Yuan Xu

    The aim of this article is to establish two-sided Gaussian bounds for the heat kernels on the unit ball and simplex in \({{\mathbb {R}}}^n\), and in particular on the interval, generated by classical differential operators whose eigenfunctions are algebraic polynomials. To this end we develop a general method that employs the natural relation of such operators with weighted Laplace operators on suitable

    更新日期:2020-04-18
  • Rhodonea Curves as Sampling Trajectories for Spectral Interpolation on the Unit Disk
    Constr. Approx. (IF 1.146) Pub Date : 2020-01-27
    Wolfgang Erb

    Rhodonea curves are classical planar curves in the unit disk with the characteristic shape of a rose. In this work, we use these rose curves as sampling trajectories to create novel nodes for spectral interpolation on the disk. By generating the interpolation spaces with a parity-modified Chebyshev–Fourier basis, we will prove the unisolvence of the interpolation on the rhodonea nodes. Properties such

    更新日期:2020-04-18
  • Besov Spaces Induced by Doubling Weights
    Constr. Approx. (IF 1.146) Pub Date : 2020-01-22
    Atte Reijonen

    Let \(1\leqslant p<\infty \), \(0

    更新日期:2020-04-18
  • Existence of Meromorphic Solutions of First-Order Difference Equations
    Constr. Approx. (IF 1.146) Pub Date : 2019-12-17
    Risto Korhonen, Yueyang Zhang

    It is shown that if $$\begin{aligned} f(z+1)^n=R(z,f), \end{aligned}$$ where R(z, f) is rational in f with meromorphic coefficients and \(\deg _f(R(z,f))=n\), has an admissible meromorphic solution, then either f satisfies a difference linear or Riccati equation with meromorphic coefficients, or the equation above can be transformed into one in a list of ten equations with certain meromorphic or algebroid

    更新日期:2019-12-17
  • Entropy of Convex Functions on ℝ d.
    Constr. Approx. Pub Date : 2018-04-17
    Fuchang Gao,Jon A Wellner

    Let Ω be a bounded closed convex set in ℝ d with non-empty interior, and let 𝒞 r (Ω) be the class of convex functions on Ω with Lr -norm bounded by 1. We obtain sharp estimates of the ε-entropy of 𝒞 r (Ω) under Lp (Ω) metrics, 1 ≤ p < r ≤ ∞. In particular, the results imply that the universal lower bound ε-d/2 is also an upper bound for all d-polytopes, and the universal upper bound of [Formula:

    更新日期:2019-11-01
  • Moment Preserving Local Spline Projection Operators
    Constr. Approx. (IF 1.146) Pub Date : 2019-07-15
    Martin Campos Pinto

    This article describes an elementary construction of a dual basis for nonuniform B-splines that is local, \(L^\infty \)-stable, and reproduces polynomials of any prescribed degree. This allows one to define local projection operators with near-optimal approximation properties in any \(L^q\), \(1 \le q \le \infty \), and high order moment preserving properties. As the dual basis functions share the

    更新日期:2019-07-15
  • Rigidity of the Hamburger and Stieltjes Moment Sequences
    Constr. Approx. (IF 1.146) Pub Date : 2019-06-25
    Alexander Dyachenko

    This paper aims at finding conditions on a Hamburger or Stieltjes moment sequence, under which the change of at most a finite number of its entries produces another sequence of the same type. It turns out that a moment sequence allows all small enough variations of this kind precisely when it is indeterminate. We also show that a determinate moment sequence has the finite index of determinacy if and

    更新日期:2019-06-25
  • Asymptotic Greediness of the Haar System in the Spaces $$L_p[0,1]$$Lp[0,1] , $$1
    Constr. Approx. (IF 1.146) Pub Date : 2019-05-28
    Fernando Albiac, José L. Ansorena, Pablo M. Berná

    Our aim in this paper is to attain a sharp asymptotic estimate for the greedy constant \(C_{g}[\mathcal {H}^{(p)},L_p]\) of the (normalized) Haar system \(\mathcal {H}^{(p)}\) in \(L_{p}[0,1]\) for \(1

    更新日期:2019-05-28
  • Morrey Sequence Spaces: Pitt’s Theorem and Compact Embeddings
    Constr. Approx. (IF 1.146) Pub Date : 2019-03-28
    Dorothee D. Haroske, Leszek Skrzypczak

    Morrey (function) spaces and, in particular, smoothness spaces of Besov–Morrey or Triebel–Lizorkin–Morrey type have enjoyed a lot of interest recently. Here we turn our attention to Morrey sequence spaces \(m_{u,p}=m_{u,p}(\mathbb {Z}^d)\), \(0

    更新日期:2019-03-28
Contents have been reproduced by permission of the publishers.
导出
全部期刊列表>>
Springer化学材料学
骄傲月
如何通过Nature平台传播科研成果
跟Nature、Science文章学绘图
隐藏1h前已浏览文章
中洪博元
课题组网站
新版X-MOL期刊搜索和高级搜索功能介绍
ACS材料视界
x-mol收录
南开大学
朱守非
廖良生
郭东升
汪铭
伊利诺伊大学香槟分校
徐明华
中山大学化学工程与技术学院
试剂库存
天合科研
down
wechat
bug