Journal of Approximation Theory最新文献

Sharp iteration asymptotics for transfer operators induced by greedy β-expansions 由贪婪β-展开诱导的转移算子的尖锐迭代渐近性

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-09-03 DOI: 10.1016/j.jat.2025.106234

Horia D. Cornean, Kasper S. Sørensen

引用次数: 0

Nevai’s condition for measures with unbounded supports 具有无界支撑的测度的内瓦伊条件

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-09-03 DOI: 10.1016/j.jat.2025.106232

Grzegorz Świderski

引用次数: 0

Asymptotics of the Humbert functions Ψ1 and Ψ2 Humbert函数的渐近性Ψ1和Ψ2

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-09-03 DOI: 10.1016/j.jat.2025.106233

Peng-Cheng Hang , Malte Henkel , Min-Jie Luo

引用次数: 0

A characterization of completely alternating functions 完全交替函数的表征

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-08-20 DOI: 10.1016/j.jat.2025.106230

Monojit Bhattacharjee , Rajkamal Nailwal

引用次数: 0

Widom factors in ℂn 智慧因子

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-08-19 DOI: 10.1016/j.jat.2025.106227

Gökalp Alpan , Turgay Bayraktar , Norm Levenberg

{"title":"Widom factors in ℂn","authors":"Gökalp Alpan , Turgay Bayraktar , Norm Levenberg","doi":"10.1016/j.jat.2025.106227","DOIUrl":"10.1016/j.jat.2025.106227","url":null,"abstract":"<div><div>We generalize the theory of Widom factors to the <span><math><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> setting. We define Widom factors of compact subsets <span><math><mrow><mi>K</mi><mo>⊂</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> associated with multivariate orthogonal polynomials and weighted Chebyshev polynomials. We show that on product subsets <span><math><mrow><mi>K</mi><mo>=</mo><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>×</mo><mo>⋯</mo><mo>×</mo><msub><mrow><mi>K</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></math></span> of <span><math><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, where each <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> is a non-polar compact subset of <span><math><mi>ℂ</mi></math></span>, these quantities have universal lower bounds which directly extend one dimensional results. Under the additional assumption that each <span><math><msub><mrow><mi>K</mi></mrow><mrow><mi>j</mi></mrow></msub></math></span> is a subset of the real line, we provide improved lower bounds for Widom factors for some weight functions <span><math><mi>w</mi></math></span>; in particular, for the case <span><math><mrow><mi>w</mi><mo>≡</mo><mn>1</mn></mrow></math></span>. Finally, we define the Mahler measure of a multivariate polynomial relative to <span><math><mrow><mi>K</mi><mo>⊂</mo><msup><mrow><mi>ℂ</mi></mrow><mrow><mi>n</mi></mrow></msup></mrow></math></span> and obtain lower bounds for this quantity on product sets.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"313 ","pages":"Article 106227"},"PeriodicalIF":0.6,"publicationDate":"2025-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144887235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

The sequence of partial sums of a unimodular power series is not ultraflat 单模幂级数的部分和序列不是超平坦的

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-08-19 DOI: 10.1016/j.jat.2025.106219

Tamás Erdélyi

引用次数: 0

Comparing the degree of constrained and unconstrained trigonometric approximation 比较有约束和无约束三角逼近的程度

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-08-07 DOI: 10.1016/j.jat.2025.106220

D. Leviatan , I. Shevchuk , V. Shevchuk

引用次数: 0

Polynomial approximation in L2 with the double-sided exponential weight via complex analysis 通过复分析，用双面指数权在L2中的多项式近似

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-08-06 DOI: 10.1016/j.jat.2025.106218

Pierre Bizeul , Boaz Klartag

引用次数: 0

On positive Jacobi matrices with compact inverses 关于具有紧逆的正雅可比矩阵

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-07-30 DOI: 10.1016/j.jat.2025.106217

Pavel Šťovíček , Grzegorz Świderski

{"title":"On positive Jacobi matrices with compact inverses","authors":"Pavel Šťovíček , Grzegorz Świderski","doi":"10.1016/j.jat.2025.106217","DOIUrl":"10.1016/j.jat.2025.106217","url":null,"abstract":"<div><div>We consider positive Jacobi matrices <span><math><mi>J</mi></math></span> with compact inverses and consequently with purely discrete spectra. A number of properties of the corresponding sequence of orthogonal polynomials is studied including the convergence of their zeros, the vague convergence of the zero counting measures and of the Christoffel–Darboux kernels on the diagonal. Particularly, if the inverse of <span><math><mi>J</mi></math></span> belongs to some Schatten class, we identify the asymptotic behavior of the sequence of orthogonal polynomials and express it in terms of its regularized characteristic function. In the even more special case when the inverse of <span><math><mi>J</mi></math></span> belongs to the trace class, we derive various formulas for the orthogonality measure, eigenvectors of <span><math><mi>J</mi></math></span> as well as for the functions of the second kind and related objects. These general results are given a more explicit form in the case when <span><math><mrow><mo>−</mo><mi>J</mi></mrow></math></span> is a generator of a Birth–Death process. Among others, we provide a formula for the trace of the inverse of <span><math><mi>J</mi></math></span>. We illustrate our results by introducing and studying a modification of the <span><math><mi>q</mi></math></span>-Laguerre polynomials corresponding to a determinate moment problem.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"313 ","pages":"Article 106217"},"PeriodicalIF":0.6,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144763703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Construction and approximation properties of exact neural network interpolation operators activated by entire functions 全函数激活的精确神经网络插值算子的构造及逼近性质

IF 0.6 3区数学

Journal of Approximation Theory Pub Date : 2025-07-28 DOI: 10.1016/j.jat.2025.106215

Dansheng Yu

{"title":"Construction and approximation properties of exact neural network interpolation operators activated by entire functions","authors":"Dansheng Yu","doi":"10.1016/j.jat.2025.106215","DOIUrl":"10.1016/j.jat.2025.106215","url":null,"abstract":"<div><div>The construction and approximation properties of exact neural network interpolation are the important and challenging topics on approximation by neural networks. Most research on exact neural network interpolation has focused on establishing existence, with very few specifically constructed interpolation neural networks proposed. The main purpose of the present paper is to provide a method for directly constructing exact neural network interpolation operators, which has the advantages that all the components in the neural network operators are explicitly known, such as the coefficients, the weights and the thresholds. By employing some important methods in approximation theory, such as the equivalence between the <span><math><mrow><mi>K</mi><mo>−</mo></mrow></math></span>functional and the modulus of continuity of the function, Berens–Lorentz Lemma, and two useful estimates of the derivatives of the operators, we establish both the direct and the converse results of approximation by the new interpolation operators, and thus obtain an equivalence characterization theorem. We also introduce a type of neural network interpolation operators with four layers and a type of max-product neural network operators, rigorously analyzing their approximation properties.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"312 ","pages":"Article 106215"},"PeriodicalIF":0.6,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144721942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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