Constructive Approximation最新文献_第2页

Non-polynomial q-Askey Scheme: Integral Representations, Eigenfunction Properties, and Polynomial Limits 非多项式 q-Askey 方案：积分表示、特征函数特性和多项式极限

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-03-11 DOI: 10.1007/s00365-024-09682-4

引用次数: 0

Asymptotics of Chebyshev Rational Functions with Respect to Subsets of the Real Line 切比雪夫有理函数相对于实线子集的渐近性

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-03-09 DOI: 10.1007/s00365-023-09670-0

Benjamin Eichinger, Milivoje Lukić, Giorgio Young

引用次数: 0

Optimal Rates of Approximation by Shallow ReLU $$^k$$ Neural Networks and Applications to Nonparametric Regression 浅 ReLU $$^k$$ 神经网络的最佳逼近率及其在非参数回归中的应用

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-02-26 DOI: 10.1007/s00365-024-09679-z

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引用次数: 0

Sharp Bernstein Inequalities on Simplex 单纯形上的锐伯恩斯坦不等式

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-02-24 DOI: 10.1007/s00365-024-09680-6

Yan Ge, Yuan Xu

引用次数: 0

Dirac Operators with Exponentially Decaying Entropy 熵指数衰减的狄拉克算子

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-02-21 DOI: 10.1007/s00365-024-09678-0

Pavel Gubkin

引用次数: 0

An Extremal Problem for the Bergman Kernel of Orthogonal Polynomials 正交多项式的伯格曼核的极值问题

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-01-30 DOI: 10.1007/s00365-023-09677-7

S. Charpentier, N. Levenberg, F. Wielonsky

引用次数: 0

Loewner Theory for Bernstein Functions I: Evolution Families and Differential Equations 伯恩斯坦函数的卢瓦纳理论 I：演化族和微分方程

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-01-22 DOI: 10.1007/s00365-023-09675-9

Pavel Gumenyuk, Takahiro Hasebe, José-Luis Pérez

{"title":"Loewner Theory for Bernstein Functions I: Evolution Families and Differential Equations","authors":"Pavel Gumenyuk, Takahiro Hasebe, José-Luis Pérez","doi":"10.1007/s00365-023-09675-9","DOIUrl":"https://doi.org/10.1007/s00365-023-09675-9","url":null,"abstract":"One-parameter semigroups of holomorphic functions appear naturally in various applications of Complex Analysis, and in particular, in the theory of (temporally) homogeneous branching processes. A suitable analogue of one-parameter semigroups in the inhomogeneous setting is the notion of a (reverse) evolution family. In this paper we study evolution families formed by Bernstein functions, which play the role of Laplace exponents for inhomogeneous continuous-state branching processes. In particular, we characterize all Herglotz vector fields that generate such evolution families and give a complex-analytic proof of a qualitative description equivalent to Silverstein’s representation formula for the infinitesimal generators of one-parameter semigroups of Bernstein functions. We also establish a sufficient condition for families of Bernstein functions, satisfying the algebraic part in the definition of an evolution family, to be absolutely continuous and hence to be described as solutions to the generalized Loewner–Kufarev differential equation. Most of these results are then applied in the sequel paper [35] to study continuous-state branching processes.","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"63 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139517810","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the Definition of Higher Gamma Functions 论高伽马函数的定义

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-01-20 DOI: 10.1007/s00365-023-09674-w

Ricardo Pérez-Marco

引用次数: 0

Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces 与同质高阶椭圆算子和球准巴纳赫函数空间相关的哈代空间的最大函数和里兹变换特性

IF 2.7 2区数学

Constructive Approximation Pub Date : 2024-01-09 DOI: 10.1007/s00365-023-09676-8

Xiaosheng Lin, Dachun Yang, Sibei Yang, Wen Yuan

{"title":"Maximal Function and Riesz Transform Characterizations of Hardy Spaces Associated with Homogeneous Higher Order Elliptic Operators and Ball Quasi-Banach Function Spaces","authors":"Xiaosheng Lin, Dachun Yang, Sibei Yang, Wen Yuan","doi":"10.1007/s00365-023-09676-8","DOIUrl":"https://doi.org/10.1007/s00365-023-09676-8","url":null,"abstract":"Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients on ({mathbb {R}}^n) and X a ball quasi-Banach function space on ({mathbb {R}}^n) satisfying some mild assumptions. Denote by (H_{X,, L}({mathbb {R}}^n)) the Hardy space, associated with both L and X, which is defined via the Lusin area function related to the semigroup generated by L. In this article, the authors establish both the maximal function and the Riesz transform characterizations of (H_{X,, L}({mathbb {R}}^n)). The results obtained in this article have a wide range of generality and can be applied to the weighted Hardy space, the variable Hardy space, the mixed-norm Hardy space, the Orlicz–Hardy space, the Orlicz-slice Hardy space, and the Morrey–Hardy space, associated with L. In particular, even when L is a second order divergence form elliptic operator, both the maximal function and the Riesz transform characterizations of the mixed-norm Hardy space, the Orlicz-slice Hardy space, and the Morrey–Hardy space, associated with L, obtained in this article, are completely new.","PeriodicalId":50621,"journal":{"name":"Constructive Approximation","volume":"4 1","pages":""},"PeriodicalIF":2.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139422246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Complete Minimal Logarithmic Energy Asymptotics for Points in a Compact Interval: A Consequence of the Discriminant of Jacobi Polynomials 紧凑区间内点的完全最小对数能量渐近线：雅可比多项式判别式的后果

IF 2.7 2区数学

Constructive Approximation Pub Date : 2023-12-30 DOI: 10.1007/s00365-023-09673-x

J. S. Brauchart

引用次数: 0