Journal of Approximation Theory最新文献_第8页

Littlewood–Paley–Rubio de Francia inequality for unbounded Vilenkin systems 源于“本拉登系统”的困境

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-11-29 DOI: 10.1016/j.jat.2023.106006

Anton Tselishchev

引用次数: 0

The sharp Landau–Kolmogorov inequality for the set ‖y′‖2, ‖y‖1, ‖y+′′‖∞ on the real line 在实线上设置“y′‖2，‖y′‖1，‖y+”‖∞时的尖锐Landau-Kolmogorov不等式

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-11-21 DOI: 10.1016/j.jat.2023.105996

N.S. Payuchenko

引用次数: 0

Coefficient-based regularized distribution regression 基于系数的正则化分布回归

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-11-04 DOI: 10.1016/j.jat.2023.105995

Yuan Mao , Lei Shi , Zheng-Chu Guo

{"title":"Coefficient-based regularized distribution regression","authors":"Yuan Mao , Lei Shi , Zheng-Chu Guo","doi":"10.1016/j.jat.2023.105995","DOIUrl":"https://doi.org/10.1016/j.jat.2023.105995","url":null,"abstract":"<div><p>In this paper, we consider the coefficient-based regularized distribution regression which aims to regress from probability measures to real-valued responses over a reproducing kernel Hilbert space (RKHS), where the regularization is put on the coefficients and kernels are assumed to be indefinite. The algorithm involves two stages of sampling, the first stage sample consists of distributions and the second stage sample is obtained from these distributions. The asymptotic behavior of the algorithm is comprehensively studied across different regularity ranges of the regression function. Explicit learning rates are derived by using kernel mean embedding and integral operator techniques. We obtain the optimal rates under some mild conditions, which match the one-stage sampled minimax optimal rate. Compared with the kernel methods for distribution regression in existing literature, the algorithm under consideration does not require the kernel to be symmetric or positive semi-definite and hence provides a simple paradigm for designing indefinite kernel methods, which enriches the theme of the distribution regression. To the best of our knowledge, this is the first result for distribution regression with indefinite kernels, and our algorithm can improve the learning performance against saturation effect.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"297 ","pages":"Article 105995"},"PeriodicalIF":0.9,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92045503","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

Triebel–Lizorkin regularity and bi-Lipschitz maps: Composition operator and inverse function regularity triiebel - lizorkin正则和bi-Lipschitz映射:复合算子和逆函数正则

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-18 DOI: 10.1016/j.jat.2023.105985

Martí Prats

引用次数: 1

Mean convergence of Fourier–Akhiezer–Chebyshev series Fourier–Akhiezer–Chebyshev级数的平均收敛性

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-11 DOI: 10.1016/j.jat.2023.105984

Manuel Bello-Hernández , Alejandro del Campo López

引用次数: 0

Richard S. Varga October 9, 1928 – February 25, 2022 Richard S.Varga 1928年10月9日至2022年2月25日

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-05 DOI: 10.1016/j.jat.2023.105971

Vladimir Andrievskii, András Kroó, József Szabados

引用次数: 0

Discrete harmonic analysis associated with Jacobi expansions III: The Littlewood–Paley–Stein gk-functions and the Laplace type multipliers 与Jacobi展开相关的离散调和分析III：Littlewood–Paley–Stein gk函数和拉普拉斯型乘法器

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-01 DOI: 10.1016/j.jat.2023.105940

Alberto Arenas, Óscar Ciaurri, Edgar Labarga

引用次数: 0

Explicit expressions and computational methods for the Fortet–Mourier distance of positive measures to finite weighted sums of Dirac measures Dirac测度有限加权和正测度的Fortet-Mourier距离的显式表达式和计算方法

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-01 DOI: 10.1016/j.jat.2023.105947

Sander C. Hille , Esmée S. Theewis

引用次数: 0

H-sets for kernel-based spaces 基于核的空间的H-集

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-01 DOI: 10.1016/j.jat.2023.105942

R. Schaback

引用次数: 0

Approximation error for neural network operators by an averaged modulus of smoothness 神经网络算子的平滑平均模数逼近误差

IF 0.9 3区数学

Journal of Approximation Theory Pub Date : 2023-10-01 DOI: 10.1016/j.jat.2023.105944

Danilo Costarelli

{"title":"Approximation error for neural network operators by an averaged modulus of smoothness","authors":"Danilo Costarelli","doi":"10.1016/j.jat.2023.105944","DOIUrl":"10.1016/j.jat.2023.105944","url":null,"abstract":"<div><p>In the present paper we establish estimates for the error of approximation (in the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>-norm) achieved by neural network (NN) operators. The above estimates have been given by means of an averaged modulus of smoothness introduced by Sendov and Popov, also known with the name of <span><math><mi>τ</mi></math></span>-modulus, in case of bounded and measurable functions on the interval <span><math><mrow><mo>[</mo><mo>−</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span>. As a consequence of the above estimates, we can deduce an <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span> convergence theorem for the above family of NN operators in case of functions which are bounded, measurable, and Riemann integrable on the above interval. In order to reach the above aims, we preliminarily establish a number of results; among them we can mention an estimate for the <span><math><mi>p</mi></math></span>-norm of the operators, and an asymptotic type theorem for the NN operators in case of functions belonging to Sobolev spaces.</p></div>","PeriodicalId":54878,"journal":{"name":"Journal of Approximation Theory","volume":"294 ","pages":"Article 105944"},"PeriodicalIF":0.9,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44291449","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