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Constructive Mathematical Analysis最新文献

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Isomorphism problem in a special class of Banach function algebras and its application 一类特殊Banach函数代数中的同构问题及其应用
Constructive Mathematical Analysis Pub Date : 2021-08-16 DOI: 10.33205/cma.952056
Kiyoshi Shirayanagi
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引用次数: 1
van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups 实直线的vander-Corput不等式和可调和群的Wiener-Wintner定理
Constructive Mathematical Analysis Pub Date : 2021-07-12 DOI: 10.33205/cma.1029202
E. Abdalaoui
{"title":"van der Corput inequality for real line and Wiener-Wintner theorem for amenable groups","authors":"E. Abdalaoui","doi":"10.33205/cma.1029202","DOIUrl":"https://doi.org/10.33205/cma.1029202","url":null,"abstract":"We extend the classical van der Corput inequality to the real line. As a consequence, we obtain a simple proof of the Wiener-Wintner theorem for the $mathbb{R}$-action which assert that for any family of maps $(T_t)_{t in mathbb{R}}$ acting on the Lebesgue measure space $(Omega,{cal {A}},mu)$ where $mu$ is a probability measure and for any $tin mathbb{R}$, $T_t$ is measure-preserving transformation on measure space $(Omega,{cal {A}},mu)$ with $T_t circ T_s =T_{t+s}$, for any $t,sin mathbb{R}$. Then, for any $f in L^1(mu)$, there is a a single null set off which $displaystyle lim_{T rightarrow +infty} frac1{T}int_{0}^{T} f(T_tomega) e^{2 i pi theta t} dt$ exists for all $theta in mathbb{R}$. We further present the joining proof of the amenable group version of Wiener-Wintner theorem due to Weiss and Ornstein.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48384265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians Gaussians广义Aitken积分的矩阵值正定核
Constructive Mathematical Analysis Pub Date : 2021-06-26 DOI: 10.33205/cma.964096
V. Menegatto, C. P. Oliveira
{"title":"Matrix valued positive definite kernels related to the generalized Aitken's integral for Gaussians","authors":"V. Menegatto, C. P. Oliveira","doi":"10.33205/cma.964096","DOIUrl":"https://doi.org/10.33205/cma.964096","url":null,"abstract":"We introduce a method to construct general multivariate positive definite kernels on a nonempty set X that employs a prescribed bounded completely monotone function and special multivariate functions on X. The method is consistent with a generalized version of Aitken’s integral formula for Gaussians. In the case where X is a cartesian product, the method produces nonseparable positive definite kernels that may be useful in multivariate interpolation. In addition, it can be interpreted as an abstract multivariate generalization of the well-established Gneiting’s model for constructing space-time covariances commonly cited in the literature. Many parametric models discussed in statistics can be interpreted as particular cases of the method.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41673806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
APROXIMATION IN WEIGHTED SPACES OF VECTOR FUNCTIONS 向量函数在加权空间中的逼近
Constructive Mathematical Analysis Pub Date : 2021-02-22 DOI: 10.33205/CMA.825986
G. Păltineanu, I. Bucur
{"title":"APROXIMATION IN WEIGHTED SPACES OF VECTOR FUNCTIONS","authors":"G. Păltineanu, I. Bucur","doi":"10.33205/CMA.825986","DOIUrl":"https://doi.org/10.33205/CMA.825986","url":null,"abstract":"In this paper, we present the duality theory for general weighted space of vector functions. We mention that a characterization of the dual of a weighted space of vector functions in the particular case $V subset C^{+} (X)$ is mentioned by J. B. Prolla in [6]. Also, we extend de Branges lemma in this new setting for convex cones of a weighted spaces of vector functions (Theorem 4.2). Using this theorem, we find various approximations results for weighted spaces of vector functions: Theorems 4.2-4.6 as well as Corollary 4.3. We mention also that a brief version of this paper, in the particular case $V subset C^{+} (X)$, is presented in [3], Chapter 2, subparagraph 2.5.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69532123","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces 多变量抽样Kantorovich算子：Orlicz空间中的定量估计
Constructive Mathematical Analysis Pub Date : 2021-02-16 DOI: 10.33205/CMA.876890
L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti
{"title":"Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces","authors":"L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini, G. Vinti","doi":"10.33205/CMA.876890","DOIUrl":"https://doi.org/10.33205/CMA.876890","url":null,"abstract":"In this paper, we establish a quantitative estimate for multivariate sampling Kantorovich operators by means of the modulus of continuity in the general setting of Orlicz spaces. As a consequence, the qualitative order of convergence can be obtained, in case of functions belonging to suitable Lipschitz classes. In the particular instance of L^p-spaces, using a direct approach, we obtain a sharper estimate than that one that can be deduced from the general case.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48360133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 10
Some numerical applications of generalized Bernstein operators 广义Bernstein算子的一些数值应用
Constructive Mathematical Analysis Pub Date : 2021-02-12 DOI: 10.33205/CMA.868272
D. Occorsio, M. Russo, W. Themistoclakis
{"title":"Some numerical applications of generalized Bernstein operators","authors":"D. Occorsio, M. Russo, W. Themistoclakis","doi":"10.33205/CMA.868272","DOIUrl":"https://doi.org/10.33205/CMA.868272","url":null,"abstract":"In this paper some recent applications of the so-called Generalized Bernstein polynomials are collected. This polynomial sequence is constructed by means of the samples of a continuous function f on equispaced points of [0; 1] and depends on an additional parameter which yields the remarkable property of improving the rate of convergence to the function f, according with the smoothness of f. This means that the sequence does not suffer of the saturation phenomena occurring by using the classical Bernstein polynomials or arising in piecewise polynomial approximation. The applications considered here deal with the numerical integration and the simultaneous approximation. Quadrature rules on equidistant nodes of [0; 1] are studied for the numerical computation of ordinary integrals in one or two dimensions, and usefully employed in Nystrom methods for solving Fredholm integral equations. Moreover, the simultaneous approximation of the Hilbert transform and its derivative (the Hadamard transform) is illustrated. For all the applications, some numerical details are given in addition to the error estimates, and the proposed approximation methods have been implemented providing numerical tests which confirm the theoretical estimates. Some open problems are also introduced.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Riemann Integrals 黎曼积分
Constructive Mathematical Analysis Pub Date : 2021-02-01 DOI: 10.1142/9789811221644_0004
{"title":"Riemann Integrals","authors":"","doi":"10.1142/9789811221644_0004","DOIUrl":"https://doi.org/10.1142/9789811221644_0004","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75930315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Metric Spaces and Limits for Sequences 序列的度量空间和极限
Constructive Mathematical Analysis Pub Date : 2021-02-01 DOI: 10.1142/9789811221644_0001
{"title":"Metric Spaces and Limits for Sequences","authors":"","doi":"10.1142/9789811221644_0001","DOIUrl":"https://doi.org/10.1142/9789811221644_0001","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86547024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
FRONT MATTER 前页
Constructive Mathematical Analysis Pub Date : 2021-02-01 DOI: 10.1142/9789811221644_fmatter
{"title":"FRONT MATTER","authors":"","doi":"10.1142/9789811221644_fmatter","DOIUrl":"https://doi.org/10.1142/9789811221644_fmatter","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85150906","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
BACK MATTER 回到问题
Constructive Mathematical Analysis Pub Date : 2021-02-01 DOI: 10.1142/9789811221644_bmatter
{"title":"BACK MATTER","authors":"","doi":"10.1142/9789811221644_bmatter","DOIUrl":"https://doi.org/10.1142/9789811221644_bmatter","url":null,"abstract":"","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":"63 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90718150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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