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Alatancang Chen

Publications and source records attributed to Alatancang Chen.

7 recordsLinked to original sources
arXiv2018

Upper semi-Weyl and upper semi-Browder spectra of unbounded upper triangular operator matrices

In this paper, we study the unbounded upper triangular operator matrix with diagonal domain. Some sufficient and necessary conditions are given under which upper semi-Weyl spectrum (resp. upper semi-Browder spectrum) of such operator matrix is equal to the union of the upper semi-Weyl spectra (resp. the upper semi-Browder spectra) of its diagonal entries. As an application, the corresponding spectral properties of Hamiltonian operator matrix are obtained.

math.SP↗
arXiv2016

The invertibility of 2X2 operator matrices

In this paper the properties of right invertible row operators, i.e., of 1X2 surjective operator matrices are studied. This investigation is based on a specific space decomposition. Using this decomposition, we characterize the invertibility of a 2X2 operator matrix. As an application, the invertibility of Hamiltonian operator matrices is investigated.

math.FA↗
arXiv2016

Series solutions to the cauchy problem for partial differential equations

The method of separation of variables can be used to solve many separable linear partial differential equations (LPDEs). Moreover, variable separation solutions usually are some trigonometric series. In the paper, base on some ideas of this method, we introduce a new technique to solve the Cauchy problem for some LPDEs with the initial conditions consisting of some trigonometric series, power series and exponential series. Then many LPDEs which are not separable are solved, such as some second order elliptic equations, Stokes equations and so on. In addition, the solutions of them can be expressed by trigonometric series, power series or exponential series. Moreover, by using power amd exponential series and an iterative method, we can solve many LPDEs and nonlinear PDEs for the first time.

math.AP↗
arXiv2014

Some basic properties of block operator matrices

General approach to the multiplication or adjoint operation of $2\times 2$ block operator matrices with unbounded entries are founded. Furthermore, criteria for self-adjointness of block operator matrices based on their entry operators are established.

math.FA↗
arXiv2013

On symplectic self-adjointness of Hamiltonian operator matrices

Symplectic self-adjointness of Hamiltonian operator matrices is studied, which arises in symplectic elasticity and optimal control. For the cases of diagonal domain and off-diagonal domain, necessary and sufficient conditions are shown. The proofs use Frobenius-Schur fractorizations of unbounded operator matrices. Under additional assumptions, sufficient conditions based on perturbation method are obtained. The theory is applied to a problem in symplectic elasticity.

math.FA↗
arXiv2013

On invertible nonnegative Hamiltonian operator matrices

Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operators to be invertible are obtained; so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli operator matrices and nonnegative Hamiltonian matrices.

math.FA↗