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Asymptotic and Partial Asymptotic Hankel Operators on H^2(D^n)

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Acta Mathematica Sinica,English Series 2019年第11期35卷 1729-1740页

作者： Anuradha GUPTA Bhawna GUPTA Department of Mathematics Delhi College of Arts and CommerceNetaji NagarUniversity of DelhiDelhiIndia Department of Mathematics University of DelhiDelhiIndia

In this paper,we generalize the concept of asymptotic Hankel operators on H2(D)to the Hardy space H2(Dn)(over polydisk)in terms of asymptotic Hankel and partial asymptotic Hankel operators and investigate some properties in case of its weak and strong convergence.Meanwhile,we introduce ith-partial Hankel operators on H2(Dn)and obtain a characterization of its compactness for n>1.Our main results include the containment of Toeplitz algebra in the collection of all strong partial asymptotic Hankel operators on H2(Dn).It is also shown that a Toeplitz operator with symbolφis asymptotic Hankel if and only if φ is holomorphic function in L∞(Tn).

关键词： Hankel operator Asymptotic Hankel operator partial asymptotic Hankel operator i(th)-partial Hankel operator i(th)-partial big Hankel operator

Application of Hankel Dynamic Mode Decomposition for Wide Area Monitoring of Subsynchronous Resonance

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Energy Engineering 2023年第4期120卷 851-867页

作者： Lei Wang Tiecheng Li Hui Fan Xuekai Hu Lin Yang Xiaomei Yang State Grid Hebei Electric Power Research Institute Shijiazhuang050021China State Grid Hebei Electric Power Company Shijiazhuang050021China The College of Electrical Engineering Sichuan UniversityChengdu610065China

In recent years,subsynchronous resonance(SSR)has frequently occurred in DFIG-connected series-compensated systems.For the analysis and prevention,it is of great importance to achieve wide area monitoring of the incident.This paper presents a Hankel dynamic mode decomposition(DMD)method to identify SSR parameters using synchrophasor data.The basic idea is to employ the DMD technique to explore the subspace of Hankel matrices constructed by synchrophasors.It is analytically demonstrated that the subspace of these Hankel matrices is a combination of fundamental and SSR modes.Therefore,the SSR parameters can be calculated once the modal parameter is extracted.Compared with the existing method,the presented work has better dynamic performances as it requires much less data.Thus,it is more suitable for practical cases in which the SSR characteristics are timevarying.The effectiveness and superiority of the proposed method have been verified by both simulations and field data.

关键词： Hankel dynamic mode decomposition time-varying sub-synchronous oscillation synchrophasor

Third Hankel Determinant for the Inverse of Starlike and Convex Functions

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Communications in Mathematical Research 2019年第4期35卷 354-358页

作者： Guo Dong Ao En Tang Huo Xiong Liang-peng Ji You-qing Foundation Department Chuzhou Vocational and Technical CollegeChuzhouAnhui239000 School of Mathematics and Statistics Chifeng UniversityChifengInner Mongolia024000 School of Mathematics and Statistics Wuhan UniversityWuhan430072 不详

Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and... 详细信息

Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.

关键词： analytic function third Hankel determinant inverse of starlike function inverse of convex function

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基于Hankel矩阵的天线伺服系统辨识

河北省科学院学报 2016年第4期33卷 41-46页

作者：闫少雄中国电子科技集团公司第五十四研究所河北石家庄050081

天线是一个时变、非线性、复杂的动力学系统,直接建模困难较大,通常采用系统辨识的方法得到天线模型。采用伪随机序列作为辨识输入,通过解算Makov参数得到Hankel矩阵,确定模型阶次,获取天线的状态方程。对比天线模型和实际系统的响应,... 详细信息

天线是一个时变、非线性、复杂的动力学系统,直接建模困难较大,通常采用系统辨识的方法得到天线模型。采用伪随机序列作为辨识输入,通过解算Makov参数得到Hankel矩阵,确定模型阶次,获取天线的状态方程。对比天线模型和实际系统的响应,辨识模型准确度较高,满足工程应用的需求。

关键词：系统辨识天线 Hankel

Hankel and Toeplitz type operators on the unit disk

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Science China Mathematics 2002年第9期45卷 1154-1162页

作者：何建勋彭立中 Sch. of Math. and Computer Science Nanjing Normal University Nanjing 210097 China School of Mathematical Science Peking University Beijing 100871 China

Let D be the unit disk in the complex plane with the weighted measure dμβ(z) = (β+1)--π(1-|z|2)βdm(z)(β＞-1). Then L2(D,dμβ(z)) = ∞k=0(Aβk Aβk) is the orthogonal direct sum decomposition.In this paper, we d... 详细信息

关键词： Hankel type operator, Toeplitz type operator, Sp-criteria, analytic Besov space, para-commutator.

On the general expressions of finite Hankel transform

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Science China(Physics,Mechanics & Astronomy) 2010年第11期53卷 2125-2130页

作者： JIANG Quan 1,2 & GAO CunFa 1 1 College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China 2 School of Civil Engineering,Nantong University,Nantong 226019,China College of Aerospace Engineering Nanjing University of Aeronautics and Astronautics Nanjing China School of Civil Engineering Nantong University Nantong China

The general expressions of finite Hankel transform are naturally deduced with the help of the property of Bessel functions.The equations in this paper can degenerate into three kinds of boundaries since all the coefficients in the boundary conditions are taken into consideration.The results can be adopted in solving physics problems involving the finite Hankel transform.

关键词： Hankel transform bessel function finite integral

Toeplitz and Hankel Products on Bergman Spaces of the Unit Ball

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 293-310页

作者： Yufeng LU Chaomei LIU School of Mathematical Sciences Dalian University of Technology Dalian 116024 Liaoning China

作者在加权的 Bergman 空间为 Toeplitz 产品的围住的海角给一些新必要条件联合起来的球的 α2 ，在 f 和 g 在单位上是分析的的地方，成球形。Hankel 产品 H f H 在联合起来的球的加权的 Bergman 空间的 g * 被学习，并且类似于那些... 详细信息

作者在加权的 Bergman 空间为 Toeplitz 产品的围住的海角给一些新必要条件联合起来的球的 α2 ，在 f 和 g 在单位上是分析的的地方，成球形。Hankel 产品 H f H 在联合起来的球的加权的 Bergman 空间的 g * 被学习，并且类似于那些 Stroethoff 和郑的结果在统一磁盘的设置获得了被证明。

关键词：加权Bergman空间 Toeplitz 单位球 Hankel 产品胸腺细胞蛋白A 有界性

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定向偏序群上的Hankel算子(英文)

上海师范大学学报（自然科学版） 2004年第1期33卷 15-18页

作者：许庆祥姚玉武上海师范大学数理信息学院上海200234

给出了定向偏序群上Hankel算子的定义,得到了一个有界线性算子为Hankel算子的充要条件.

关键词： Hankel 算子定向偏序群

Wavelets associated with Hankel transform and their Weyl transforms

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Science China Mathematics 2004年第3期47卷 393-400页

作者： PENG Lizhong MA Ruiqin LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, China LMAM School of Mathematical Sciences Peking University Beijing China

The Hankel transform is an important transform. In this paper, westudy the wavelets associated with the Hankel transform, thendefine the Weyl transform of the wavelets. We give criteria of itsboundedness and compactne... 详细信息

关键词： Bessel function, Hankel transform, wavelets, Weyltransform, boundedness, compactness.