Journal of Approximation Theory最新文献

{"title":"Invertible and Fredholm operators on interpolation scales","authors":"Irina Asekritova ,&nbsp;Natan Kruglyak ,&nbsp;Mieczysław Mastyło","doi":"10.1016/j.jat.2025.106213","DOIUrl":"10.1016/j.jat.2025.106213","url":null,"abstract":"<div><div>We investigate the behaviour of invertible and Fredholm operators on interpolation scales constructed via a family of interpolation functors <span><math><msub><mrow><mrow><mo>{</mo><msub><mrow><mi>F</mi></mrow><mrow><mi>θ</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>θ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></msub></math></span>. This family includes both complex and real interpolation functors. Our results demonstrate, in particular, that kernels and cokernels of operators are stable on intervals of parameters <span><math><mi>θ</mi></math></span> where the operators are Fredholm. Additionally, we introduce the notion of Fredholm operators in the category of Banach couples, establishing its relevance for the obtained results.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106213"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683676","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}

{"title":"On multiplier analogues of the algebra C+H∞ on weighted rearrangement-invariant sequence spaces","authors":"Oleksiy Karlovych,&nbsp;Sandra Mary Thampi","doi":"10.1016/j.jat.2025.106223","DOIUrl":"10.1016/j.jat.2025.106223","url":null,"abstract":"&lt;div&gt;&lt;div&gt;Let &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; be a reflexive rearrangement-invariant Banach sequence space with nontrivial Boyd indices &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and let &lt;span&gt;&lt;math&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; be a symmetric weight in the intersection of the Muckenhoupt classes &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;α&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;β&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. Let &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; denote the collection of all periodic distributions &lt;span&gt;&lt;math&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/span&gt; generating bounded Laurent operators &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;L&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; on the space &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;φ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;→&lt;/mo&gt;&lt;mi&gt;ℂ&lt;/mi&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mi&gt;φ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. We show that &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; is a Banach algebra. Further, we consider the closure of trigonometric polynomials in &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; denoted by &lt;span&gt;&lt;math&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;:&lt;/mo&gt;&lt;mover&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;̂&lt;/mo&gt;&lt;/mrow&gt;&lt;/mover&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;±&lt;/mo&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mtext&gt; for &lt;/mtext&gt;&lt;mi&gt;n&lt;/mi&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. We prove that &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;C&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msubsup&gt;&lt;mrow&gt;&lt;mi&gt;H&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;X&lt;/mi&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;Z&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;w&lt;","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106223"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683609","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}

{"title":"The Calderón–Mityagin property for couples of weighted Radon measures","authors":"Per G. Nilsson","doi":"10.1016/j.jat.2025.106224","DOIUrl":"10.1016/j.jat.2025.106224","url":null,"abstract":"<div><div>The aim of this note is to introduce two new generic Banach lattice couples based on weighted spaces of continuous functions, and weighted Radon measures on the positive real-line, denoted by <span><math><mover><mrow><mi>C</mi></mrow><mo>⃗</mo></mover></math></span> and <span><math><mover><mrow><mi>M</mi></mrow><mo>⃗</mo></mover></math></span> respectively. This leads to a new approach, based on these couples, of the Sedaev–Semenov result regarding the Calderón–Mityagin property for weighted <span><math><msub><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> spaces. As a consequence is obtained a formal equivalence between the concept of <span><math><mi>K</mi></math></span> divisibility and the relative Calderón–Mityagin Property between <span><math><mover><mrow><mi>M</mi></mrow><mo>⃗</mo></mover></math></span> and general Banach couples.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106224"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683679","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}

{"title":"Nevai’s condition for measures with unbounded supports","authors":"Grzegorz Świderski","doi":"10.1016/j.jat.2025.106232","DOIUrl":"10.1016/j.jat.2025.106232","url":null,"abstract":"<div><div>We study Nevai’s condition from the theory of orthogonal polynomials on the real line. We prove that a large class of measures with unbounded Jacobi parameters satisfies Nevai’s condition locally uniformly on the support of the measure away from a finite explicit set. This allows us to give applications to relative uniform and weak asymptotics of Christoffel–Darboux kernels on the diagonal and to limit theorems for unconventionally normalized global linear statistics of orthogonal polynomial ensembles.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106232"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145050628","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}

{"title":"2-strong uniqueness of a best approximation and of minimal projections in complex polytope norms and their duals","authors":"Tomasz Kobos,&nbsp;Grzegorz Lewicki","doi":"10.1016/j.jat.2025.106245","DOIUrl":"10.1016/j.jat.2025.106245","url":null,"abstract":"<div><div>We study a property of 2-strong uniqueness of a best approximation in a class of finite-dimensional complex normed spaces, for which the unit ball is an absolutely convex hull of finite number of points and in its dual class. We prove that, contrary to the real case, these two classes do not coincide but are in fact disjoint. We provide several examples of situations in these two classes, where a uniqueness of an element of a best approximation in a given subspace implies its 2-strong uniqueness. In particular, such a property holds for approximation in an arbitrary subspace of the complex <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> space, but not of the complex <span><math><msubsup><mrow><mi>ℓ</mi></mrow><mrow><mi>∞</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> space. However, this is true in general under an additional assumption that a subspace has a real basis and an ambient complex normed space is generated by real vectors or functionals. We apply our results and related methods to establish some results concerned with 2-strongly unique minimal projections in complex normed spaces, proving among other things, that a minimal projection onto a two-dimensional subspace of an arbitrary three-dimensional complex normed space is 2-strongly unique, if its norm is greater than 1.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106245"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363620","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}

{"title":"Interpolation of functions with zero integrals over balls of fixed radius","authors":"Valery Volchkov,&nbsp;Vitaly Volchkov","doi":"10.1016/j.jat.2025.106226","DOIUrl":"10.1016/j.jat.2025.106226","url":null,"abstract":"<div><div>We investigate some interpolation problems for functions with vanishing integrals over all balls in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>\u0000 (<span><math><mrow><mi>n</mi><mo>≥</mo><mn>2</mn></mrow></math></span>) of fixed radius. In the case when the set of interpolation nodes is finite a complete solution of the multiple interpolation problem is obtained. In addition, the case when the set of interpolation nodes is infinite and not contained on some line in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> is studied for the first time. We give a sufficient condition for the solvability of interpolation problem when the set of interpolation nodes is quite rare. We note that the results of the paper are false in the case of dimension <span><math><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></math></span>.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106226"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683673","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}

{"title":"Interpolation of compact multilinear operators between quasi-Banach spaces","authors":"Fernando Cobos ,&nbsp;Luz M. Fernández-Cabrera ,&nbsp;Thomas Kühn","doi":"10.1016/j.jat.2025.106222","DOIUrl":"10.1016/j.jat.2025.106222","url":null,"abstract":"<div><div>We investigate the interpolation properties of compact multilinear operators by the real method between quasi-Banach spaces. As an application we establish a reinforced version of a multilinear Marcinkiewicz theorem.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106222"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683675","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}

{"title":"Nonlinear approximation of harmonic functions from shifts of the Newtonian kernel in BMO","authors":"Kamen G. Ivanov ,&nbsp;Pencho Petrushev","doi":"10.1016/j.jat.2025.106246","DOIUrl":"10.1016/j.jat.2025.106246","url":null,"abstract":"<div><div>We study nonlinear <span><math><mi>n</mi></math></span>-term approximation of harmonic functions on the unit ball in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup></math></span> from linear combinations of shifts of the Newtonian kernel (fundamental solution of the Laplace equation) in BMO. A Jackson estimate is established that naturally involves Besov spaces lying on the Sobolev embedding line for BMO. The method for obtaining this result is based on the construction of highly localized frames for Besov spaces and VMO on the sphere whose elements are linear combinations of a fixed number of shifts of the Newtonian kernel.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106246"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145325809","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}

{"title":"Dedication","authors":"Alexander Brudnyi,&nbsp;Natan Kruglyak,&nbsp;Mieczysław Mastyło,&nbsp;Paul Nevai,&nbsp;Amos Ron,&nbsp;Pavel Shvartsman","doi":"10.1016/j.jat.2025.106231","DOIUrl":"10.1016/j.jat.2025.106231","url":null,"abstract":"","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106231"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683678","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}

{"title":"Best approximation of constants by polynomials with integer coefficients","authors":"R. Trigub ,&nbsp;V. Volchkov","doi":"10.1016/j.jat.2025.106225","DOIUrl":"10.1016/j.jat.2025.106225","url":null,"abstract":"<div><div>What is best approximation of a non-integer number <span><math><mrow><mi>λ</mi><mo>∈</mo><mi>R</mi></mrow></math></span> by polynomials <span><math><msub><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span> of degree at most <span><math><mi>n</mi></math></span> with integer coefficients on the segment <span><math><mrow><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>]</mo></mrow><mo>⊂</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> in the uniform metric? In the paper, this old problem is solved for any rational number <span><math><mrow><mi>λ</mi><mo>=</mo><mfrac><mrow><mi>p</mi></mrow><mrow><mi>q</mi></mrow></mfrac></mrow></math></span> and a segment on the real line. The same problem is solved when the segment is replaced by a disk in <span><math><mi>ℂ</mi></math></span> and a cube in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>m</mi></mrow></msup></math></span>, both non containing integer points. Best approximation of rational numbers by polynomials with natural coefficients is considered as well. At the same time, the question of uniqueness and non-uniqueness of best approximation polynomials has also been studied. In addition, connection between theorems on best approximation to functions by polynomials with integer coefficients and integer transfinite diameter is established.</div></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"314 ","pages":"Article 106225"},"PeriodicalIF":0.6,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145683672","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}