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Constructive Mathematical Analysis最新文献

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Abstract Generalized Fractional Landau inequalities over R R上的广义分式朗道不等式
Constructive Mathematical Analysis Pub Date : 2020-10-21 DOI: 10.33205/CMA.764161
G. Anastassiou
{"title":"Abstract Generalized Fractional Landau inequalities over R","authors":"G. Anastassiou","doi":"10.33205/CMA.764161","DOIUrl":"https://doi.org/10.33205/CMA.764161","url":null,"abstract":"We present uniform and $L_p$ mixed Caputo-Bochner abstract generalized fractional Landau inequalities over $mathbb{R}$ of fractional orders $ 2 < alpha leq 3 $. These estimate the size of first and second derivatives of a composition with a  Banach space valued function over $mathbb{R}$. We give applications when $α = 2.5$.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48991874","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: 11
The A-integral and restricted Riesz transform A积分与限制Riesz变换
Constructive Mathematical Analysis Pub Date : 2020-09-01 DOI: 10.33205/cma.728156
R. Aliev, Khanim I. Nebiyeva
{"title":"The A-integral and restricted Riesz transform","authors":"R. Aliev, Khanim I. Nebiyeva","doi":"10.33205/cma.728156","DOIUrl":"https://doi.org/10.33205/cma.728156","url":null,"abstract":"It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue integrable. In this paper we prove that the restricted Riesz transform of a Lebesgue integrable function is A-integrable and the analogue of Riesz's equality holds. ABSTRACT.It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue inte-grable. In this paper, we prove that the restricted Riesz transform of a Lebesgue integrable function isA-integrableand the analogue of Riesz’s equality holds","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46431542","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
Ulam stability in real inner-product spaces 实内积空间中的Ulam稳定性
Constructive Mathematical Analysis Pub Date : 2020-09-01 DOI: 10.33205/cma.758854
Bianca Moșneguțu, A. Mǎdutǎ
{"title":"Ulam stability in real inner-product spaces","authors":"Bianca Moșneguțu, A. Mǎdutǎ","doi":"10.33205/cma.758854","DOIUrl":"https://doi.org/10.33205/cma.758854","url":null,"abstract":"Roughly speaking an equation is called Ulam stable if near each approximate solution of the equation there exists an exact solution. In this paper we prove that Cauchy-Schwarz equation, Ortogonality equation and Gram equation are Ulam stable. This paper is concerned with the Ulam stability of some classical equations arising in thecontext of inner-product spaces. For the general notion of Ulam stability see, e.q., [1]. Roughlyspeaking an equation is called Ulam stable if near every approximate solution there exists anexact solution; the precise meaning in each case presented in this paper is described in threetheorems. Related results can be found in [2, 3, 4]. See also [5] for some inequalities in innerproduct spaces.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48370366","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: 2
Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fej'er sums 三角Fejer和的强逆不等式和定量Voronovskaya型定理
Constructive Mathematical Analysis Pub Date : 2020-06-01 DOI: 10.33205/cma.653843
J. Bustamante, Lázaro Flores De Jesús
{"title":"Strong converse inequalities and quantitative Voronovskaya-type theorems for trigonometric Fej'er sums","authors":"J. Bustamante, Lázaro Flores De Jesús","doi":"10.33205/cma.653843","DOIUrl":"https://doi.org/10.33205/cma.653843","url":null,"abstract":"Let $sigma_n$ denotes the classical Fej'er operator for trigonometric expansions. For a fixed even integer $r$, we characterize the rate of convergence of the iterative operators $(I-sigma_n)^r(f)$ in terms of the modulus of continuity of order $r$ (with specific constants) in all $mathbb{L}^p$ spaces $1leq p leq infty$. In particular, the constants depend not on $p$. Moreover, we present a quantitative version of the Voronovskaya-type theorems for the operators $(I-sigma_n)^r(f)$.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48490943","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
Gneiting Class, Semi-Metric Spaces and Isometric Embeddings 类，半度量空间和等距嵌入
Constructive Mathematical Analysis Pub Date : 2020-06-01 DOI: 10.33205/cma.712049
V. Menegatto, C. Oliveira, E. Porcu
{"title":"Gneiting Class, Semi-Metric Spaces and Isometric Embeddings","authors":"V. Menegatto, C. Oliveira, E. Porcu","doi":"10.33205/cma.712049","DOIUrl":"https://doi.org/10.33205/cma.712049","url":null,"abstract":"This paper revisits the Gneiting class of positive definite kernels originally proposed as a class of covariance functions for space-time processes. Under the framework of quasi-metric spaces and isometric embeddings, the paper proposes a general and unifying framework that encompasses results provided by earlier literature. Our results allow to study the positive definiteness of the Gneiting class over products of either Euclidean spaces or high dimensional spheres and quasi-metric spaces. In turn, Gneiting's theorem is proved here by a direct construction, eluding Fourier inversion (the so-called Gneiting's lemma) and convergence arguments that are required by Gneiting to preserve an integrability assumption.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44623720","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: 13
Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $mathbf{L}$-index in Joint Variables 联合变量中有界$mathbf{L}$指数的单位球中解析向量值函数的增长估计
Constructive Mathematical Analysis Pub Date : 2020-03-01 DOI: 10.33205/CMA.650977
V. Baksa, Andriy Ivanovych Bandura, O. Skaskiv
{"title":"Growth Estimates for Analytic Vector-Valued Functions in the Unit Ball Having Bounded $mathbf{L}$-index in Joint Variables","authors":"V. Baksa, Andriy Ivanovych Bandura, O. Skaskiv","doi":"10.33205/CMA.650977","DOIUrl":"https://doi.org/10.33205/CMA.650977","url":null,"abstract":"Our results concern growth estimates for vector-valued functions of $mathbb{L}$-index in joint variables which are analytic in the unit ball.  There are deduced analogs of known growth estimates obtained early for functions analytic in the unit ball. Our estimates contain logarithm of $sup$-norm instead of logarithm modulus of the function. They describe the behavior of logarithm of norm of analytic vector-valued function on a skeleton in a bidisc by behavior of the function $mathbf{L}.$ These estimates are sharp in a general case.  The presented results are based on bidisc exhaustion of a unit ball.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45783216","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: 7
On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle 单位圆上的超几何Sobolev正交多项式族
Constructive Mathematical Analysis Pub Date : 2020-02-15 DOI: 10.33205/cma.690236
S. Zagorodnyuk
{"title":"On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle","authors":"S. Zagorodnyuk","doi":"10.33205/cma.690236","DOIUrl":"https://doi.org/10.33205/cma.690236","url":null,"abstract":"In this paper we study the following family of hypergeometric polynomials: $y_n(x) = frac{ (-1)^rho }{ n! } x^n {}_2 F_0(-n,rho;-;-frac{1}{x})$, depending on a parameter $rhoinmathbb{N}$. Differential equations of orders $rho+1$ and $2$ for these polynomials are given. A recurrence relation for $y_n$ is derived as well. Polynomials $y_n$ are Sobolev orthogonal polynomials on the unit circle with an explicit matrix measure.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43487318","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: 7
Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series 三角级数快速求和的高斯型求积公式
Constructive Mathematical Analysis Pub Date : 2019-12-01 DOI: 10.33205/cma.613948
G. Milovanović
{"title":"Quadrature Formulas of Gaussian Type for Fast Summation of Trigonometric Series","authors":"G. Milovanović","doi":"10.33205/cma.613948","DOIUrl":"https://doi.org/10.33205/cma.613948","url":null,"abstract":"A summation/integration method for fast summing trigonometric series is presented. The basic idea in this method is to transform the series to an integral with respect to some weight function on $RR_+$ and then to approximate such an integral by the appropriate quadrature formulas of Gaussian type. The construction of these quadrature rules, as well as  the corresponding orthogonal polynomials on $RR_+$, are also considered. Finally, in order to illustrate the efficiency of the presented  summation/integration method two numerical examples are included.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43907942","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: 2
Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces 一类grushin型空间中四元数漂移拉普拉斯方程的推广
Constructive Mathematical Analysis Pub Date : 2019-10-09 DOI: 10.33205/cma.1324774
Thomas Bieske, Keller Blackwell
{"title":"Generalizations of the drift Laplace equation over the quaternions in a class of Grushin-type spaces","authors":"Thomas Bieske, Keller Blackwell","doi":"10.33205/cma.1324774","DOIUrl":"https://doi.org/10.33205/cma.1324774","url":null,"abstract":"Beals, Gaveau, and Greiner established a formula for the fundamental solution to the Laplace equation with drift term in Grushin-type planes. The first author and Childers expanded these results by invoking a p-Laplace type generalization that encompasses these formulas while the authors explored a different natural generalization of the p-Laplace equation with drift term that also encompasses these formulas. In both, the drift term lies in the complex domain. We extend these results by considering a drift term in the quaternion realm and show our solutions are stable under limits as p tends to infinity.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46597067","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
Shift $lambda $-Invariant Operators Shift$lambda$-不变运算符
Constructive Mathematical Analysis Pub Date : 2019-09-01 DOI: 10.33205/CMA.544094
O. Agratini
{"title":"Shift $lambda $-Invariant Operators","authors":"O. Agratini","doi":"10.33205/CMA.544094","DOIUrl":"https://doi.org/10.33205/CMA.544094","url":null,"abstract":"The present note is devoted to a generalization of the notion of shift invariant operators that we call it $lambda $-invariant operators $(lambda ge 0)$. Some properties of this new class are presented. By using probabilistic methods, three examples are delivered.","PeriodicalId":36038,"journal":{"name":"Constructive Mathematical Analysis","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47693814","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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