In this paper, we study one class of n-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding op...In this paper, we study one class of n-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding operator norms on both LP（Rn） and BMO（Rn）.展开更多
We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive mea...We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive measure. We prove the existence of an increasing unbounded sequence of eigenvalues. The method of proof makes use of variational arguments.展开更多
First,we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary.Then we give two applications of this formula when the manifold satisfies certain geom...First,we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary.Then we give two applications of this formula when the manifold satisfies certain geometric conditions.One is a sharp lower bound for the first positive eigenvalue of the Steklov eigenvalue problem on differential forms investigated by Belishev and Sharafutdinov(2008)and Karpukhin(2019).The other one is a comparison result between the spectrum of this Steklov eigenvalue problem and the spectrum of the Hodge Laplacian on the boundary of the manifold.Besides,in the end we discuss an open problem for differential forms analogous to Escobar's conjecture(1999)for functions.展开更多
Steklov eigenvalue problem of Helmholtz equation is considered in the present paper. Steklov eigenvalue problem is reduced to a new variational formula on the boundary of a given domain, in which the self-adjoint prop...Steklov eigenvalue problem of Helmholtz equation is considered in the present paper. Steklov eigenvalue problem is reduced to a new variational formula on the boundary of a given domain, in which the self-adjoint property of the original differential operator is kept and the calculating of hyper-singular integral is avoided. A numerical example showing the efficiency of this method and an optimal error estimate are given.展开更多
We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integra...We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.展开更多
Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a pos...Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.展开更多
文摘In this paper, we study one class of n-dimensional Hardy-Steklov operators which has important applications in the technical analysis in equity markets. We establish their weighted boundedness and the corresponding operator norms on both LP（Rn） and BMO（Rn）.
文摘We will study the generalized Steklov-Robin eigenproblem (with possibly matrix weights) in which the spectral parameter is both in the system and on the boundary. The weights may be singular on subsets of positive measure. We prove the existence of an increasing unbounded sequence of eigenvalues. The method of proof makes use of variational arguments.
基金supported by the National Natural Science Foundation of the People’s Republic of China“The research of finite element methods for eigenvalue problems in inverse scattering”(12261024)。
基金supported by National Key Research and Development Program of China(Grant No.2021YFA1001800)National Natural Science Foundation of China(Grant No.12171334)。
文摘First,we establish a weighted Reilly formula for differential forms on a smooth compact oriented Riemannian manifold with boundary.Then we give two applications of this formula when the manifold satisfies certain geometric conditions.One is a sharp lower bound for the first positive eigenvalue of the Steklov eigenvalue problem on differential forms investigated by Belishev and Sharafutdinov(2008)and Karpukhin(2019).The other one is a comparison result between the spectrum of this Steklov eigenvalue problem and the spectrum of the Hodge Laplacian on the boundary of the manifold.Besides,in the end we discuss an open problem for differential forms analogous to Escobar's conjecture(1999)for functions.
文摘Steklov eigenvalue problem of Helmholtz equation is considered in the present paper. Steklov eigenvalue problem is reduced to a new variational formula on the boundary of a given domain, in which the self-adjoint property of the original differential operator is kept and the calculating of hyper-singular integral is avoided. A numerical example showing the efficiency of this method and an optimal error estimate are given.
文摘We propose a numerical method for a non-selfadjoint Steklov eigenvalue problem of the Helmholtz equation.The problem is formulated using boundary integrals.The Nyström method is employed to discretize the integral operators,which leads to a non-Hermitian generalized matrix eigenvalue problems.The spectral indicator method(SIM)is then applied to calculate the(complex)eigenvalues.The convergence is proved using the spectral approximation theory for(non-selfadjoint)compact operators.Numerical examples are presented for validation.
基金supported by National Natural Science Foundation of China(Grant Nos.11201093 and 11161012)
文摘Based on the work of Xu and Zhou(2000),this paper makes a further discussion on conforming finite elements approximation for Steklov eigenvalue problems,and proves a local a priori error estimate and a new local a posteriori error estimate in ||·||1,Ω0 norm for conforming elements eigenfunction,which has not been studied in existing literatures.
