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Classification of self-adjoint domains of odd-order differential operators with matrix theory 用矩阵理论分类奇阶微分算子的自伴随域
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0104
Mao-zhu Zhang, Xiaoling Hao, Jing Wang
{"title":"Classification of self-adjoint domains of odd-order differential operators with matrix theory","authors":"Mao-zhu Zhang, Xiaoling Hao, Jing Wang","doi":"10.1515/math-2023-0104","DOIUrl":"https://doi.org/10.1515/math-2023-0104","url":null,"abstract":"Abstract In this article, we investigate the classification of self-adjoint boundary conditions of odd-order differential operators. We obtain that for odd-order self-adjoint boundary conditions under some assumptions, there are exactly two basic types of self-adjoint boundary conditions: coupled and mixed. Moreover we determine the number of possible conditions for each type, which is different from the even-order cases. Our construction will play an important role in the canonical forms and in the spectral analysis of these operators.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44504521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Multidimensional sampling-Kantorovich operators in BV-spaces bv空间中的多维采样- kantorovich算子
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0573
L. Angeloni, G. Vinti
{"title":"Multidimensional sampling-Kantorovich operators in BV-spaces","authors":"L. Angeloni, G. Vinti","doi":"10.1515/math-2022-0573","DOIUrl":"https://doi.org/10.1515/math-2022-0573","url":null,"abstract":"Abstract The main purpose of this article is to prove a result of convergence in variation for a family of multidimensional sampling-Kantorovich operators in the case of averaged-type kernels. The setting in which we work is that one of BV-spaces in the sense of Tonelli.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48553617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2
Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications 广义Orlicz-Sobolev空间中的插值不等式及其应用
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0595
Rui Wu, Songbai Wang
{"title":"Interpolation inequalities in generalized Orlicz-Sobolev spaces and applications","authors":"Rui Wu, Songbai Wang","doi":"10.1515/math-2022-0595","DOIUrl":"https://doi.org/10.1515/math-2022-0595","url":null,"abstract":"Abstract Let m ∈ N min {mathbb{N}} and be a generalized Orlicz function. We obtained some interpolation inequalities for derivatives in generalized Orlicz-Sobolev spaces W m , φ ( R n ) {W}^{m,varphi }left({{mathbb{R}}}^{n}) . As applications, we established a compact Sobolev embedding on domain and a Landau-Kolmogorov-type inequality in generalized Orlicz spaces. And we introduced the Sobolev φ varphi -capacity and studied some of its properties.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49017020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Remarks on hyponormal Toeplitz operators with nonharmonic symbols 关于具有非调和符号的次正规Toeplitz算子的注记
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0114
Sumin Kim, Jongrak Lee
{"title":"Remarks on hyponormal Toeplitz operators with nonharmonic symbols","authors":"Sumin Kim, Jongrak Lee","doi":"10.1515/math-2023-0114","DOIUrl":"https://doi.org/10.1515/math-2023-0114","url":null,"abstract":"Abstract In this article, we present some necessary or sufficient conditions for the hyponormality of Toeplitz operator T φ {T}_{varphi } on the Bergman space A 2 ( D ) {A}^{2}left({mathbb{D}}) . In particular, we consider the Toeplitz operator T φ {T}_{varphi } with nonharmonic symbols φ varphi under certain assumptions.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49224333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering 逆散射中Steklov特征值问题的一种基于移位逆迭代的多网格离散化方法
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0607
Jiali Xie, H. Bi
{"title":"A multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering","authors":"Jiali Xie, H. Bi","doi":"10.1515/math-2022-0607","DOIUrl":"https://doi.org/10.1515/math-2022-0607","url":null,"abstract":"Abstract Numerical methods for computing Steklov eigenvalues have attracted the attention of academia for their important physical background and wide applications. In this article we discuss the multigrid discretization scheme based on the shifted inverse iteration for the Steklov eigenvalue problem in inverse scattering, and give the error estimation of the proposed scheme. In addition, on the basis of the a posteriori error indicator, we design an adaptive multigrid algorithm. Finally, we present numerical examples to show the efficiency of the proposed scheme.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47328027","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Note on differential identities on σ-prime rings with involution 有对合的σ-素环上的微分恒等式
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1142/s2811007223500050
M. Madni, M. R. Mozumder, W. Ahmed, A. Abbasi̇, A. Ramesh
{"title":"Note on differential identities on σ-prime rings with involution","authors":"M. Madni, M. R. Mozumder, W. Ahmed, A. Abbasi̇, A. Ramesh","doi":"10.1142/s2811007223500050","DOIUrl":"https://doi.org/10.1142/s2811007223500050","url":null,"abstract":"The major goal of this paper is to investigate the structure of [Formula: see text]-prime rings with involution, satisfying certain [Formula: see text]-differential identities involving [Formula: see text]-centralizing and some special type of products. We also provide an example which shows that center of [Formula: see text]-prime ring is not free from zero divisors.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"31 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76053136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications 完备CAT(0)空间中非扩张映射序列的平均遍历定理及其应用
4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0121
Sakan Termkaew, Parin Chaipunya, Fumiaki Kohsaka
{"title":"Mean ergodic theorems for a sequence of nonexpansive mappings in complete CAT(0) spaces and its applications","authors":"Sakan Termkaew, Parin Chaipunya, Fumiaki Kohsaka","doi":"10.1515/math-2023-0121","DOIUrl":"https://doi.org/10.1515/math-2023-0121","url":null,"abstract":"Abstract In this article, we prove ergodic convergence for a sequence of nonexpansive mappings in Hadamard (complete <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mi mathvariant=\"normal\">CAT</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mn>0</m:mn> </m:mrow> <m:mo>)</m:mo> </m:mrow> </m:math> {rm{CAT}}left(0) ) spaces. Our result extends the nonlinear ergodic theorem by Baillon for nonexpansive mappings from Hilbert spaces to Hadamard spaces. We further establish the standard nonlinear ergodic theorem and apply our results to the problem of finding a common fixed point of a countable family of nonexpansive mappings. Finally, we propose some applications of our results to solve convex optimization problems in Hadamard spaces.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135913321","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
On a class of stochastic differential equations driven by the generalized stochastic mixed variational inequalities 一类由广义随机混合变分不等式驱动的随机微分方程
4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2023-0109
Qiaofeng Zeng, Chao Min, Feifei Fan
{"title":"On a class of stochastic differential equations driven by the generalized stochastic mixed variational inequalities","authors":"Qiaofeng Zeng, Chao Min, Feifei Fan","doi":"10.1515/math-2023-0109","DOIUrl":"https://doi.org/10.1515/math-2023-0109","url":null,"abstract":"Abstract A new class of stochastic differential equations (SDEs) is introduced in this article, which is driven by the generalized stochastic mixed variational inequality (GS-MVI). First, the property of the solution sets of the GS-MVI is proved by Fan-Knaster-Kuratowski-Mazurkiewicz (FKKM) theorem and Aumann’s measurable selection theorem. Next, we obtain the Carathéodory property of the solution set, with which the discussed SDEs can be transformed to stochastic differential inclusions (SDIs). The solution set of the proposed SDEs is proved to be nonempty through the existence of the solutions of the corresponding SDIs by the tools of fixed point theorem.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136209861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Non-solid cone b-metric spaces over Banach algebras and fixed point results of contractions with vector-valued coefficients Banach代数上的非实心锥b-度量空间及向量值系数收缩的不动点结果
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0569
Shaoyuan Xu, Suyu Cheng, Yanying Han
{"title":"Non-solid cone b-metric spaces over Banach algebras and fixed point results of contractions with vector-valued coefficients","authors":"Shaoyuan Xu, Suyu Cheng, Yanying Han","doi":"10.1515/math-2022-0569","DOIUrl":"https://doi.org/10.1515/math-2022-0569","url":null,"abstract":"Abstract In this article, without requiring solidness of the underlying cone, a kind of new convergence for sequences in cone b b -metric spaces over Banach algebras and a new kind of completeness for such spaces, namely, wrtn-completeness, are introduced. Under the condition that the cone b b -metric spaces are wrtn-complete and the underlying cones are normal, we establish a common fixed point theorem of contractive conditions with vector-valued coefficients in the non-solid cone b b -metric spaces over Banach algebras, where the coefficients s ≥ 1 sge 1 . As consequences, we obtain a number of fixed point theorems of contractions with vector-valued coefficients, especially the versions of Banach contraction principle, Kannan’s and Chatterjea’s fixed point theorems in non-solid cone b b -metric spaces over Banach algebras. Moreover, some valid examples are presented to support our main results.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45692839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Scattering properties of Sturm-Liouville equations with sign-alternating weight and transmission condition at turning point 具有符号交替权和传递条件的Sturm-Liouville方程在转折点的散射特性
IF 1.7 4区 数学
Open Mathematics Pub Date : 2023-01-01 DOI: 10.1515/math-2022-0566
N. Coskun, Merve Görgülü
{"title":"Scattering properties of Sturm-Liouville equations with sign-alternating weight and transmission condition at turning point","authors":"N. Coskun, Merve Görgülü","doi":"10.1515/math-2022-0566","DOIUrl":"https://doi.org/10.1515/math-2022-0566","url":null,"abstract":"Abstract In this article, we focus on the scattering analysis of Sturm-Liouville type singular operator including an impulsive condition and turning point. In the classical literature, there are plenty of papers considering the positive values of the weight function in both continuous and discontinuous cases. However, this article differs from the others in terms of the impulsive condition appearing at the turning point. We generate the scattering function, resolvent operator, and discrete spectrum of the operator using the hyperbolic representations of the fundamental solutions. Finally, we create an example to show the article’s primary conclusions.","PeriodicalId":48713,"journal":{"name":"Open Mathematics","volume":" ","pages":""},"PeriodicalIF":1.7,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45957122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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