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| 1 | Structure of the spectrum of infinite dimensional Hamiltonian operators显示文摘This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty. | Alatancang | 2008 | Science China Mathematics2008，51，5： | 26 |
| 2 | Completeness in the sense of Cauchy principal value of the eigenfunction systems of infinite dimensional Hamiltonian operator显示文摘The properties of eigenvalues and eigenfunctions of the infinite dimensional Hamiltonian operators are studied, and the suffcient conditions of the completeness in the sense of Cauchy principal value of the eigenfunction systems of the infinite dimensional Hamiltonian operators are given. In the end, concrete examples are constructed to justify the effectiveness of the criterion. | Alatancang WU DeYu | 2009 | Science China Mathematics2009，52，1： | 22 |
| 3 | Spectra of Off-diagonal Infinite-Dimensional Hamiltonian Operators and Their Applications to Plane Elasticity Problems显示文摘在现在的纸,离开斜的无限维的 Hamiltonian 操作员的系列被学习。起初,我们证明光谱,连续光谱,并且点光谱的联合和操作员的剩余光谱关于真实的轴和想象的轴是对称的。然后为减少学习问题的尺寸的目的,操作符的系列被二个自我伴随操作符的产品的系列在州的空格表示。最后,上述结果被用于飞机弹性问题,它显示出结果的有实行可能。 | Alatancang | 2009 | Communications in Theoretical Physics2009，51，2： | 13 |
| 4 | Double Symplectic Eigenfunction Expansion Method of Free Vibration of Rectangular Thin Plates显示文摘The free vibration problem of rectangular thin plates is rewritten as a new upper triangular matrixdifferential system.For the associated operator matrix,we find that the two diagonal block operators are Hamiltonian.Moreover,the existence and completeness of normed symplectic orthogonal eigenfunction systems of these two blockoperators are demonstrated.Based on the completeness,the general solution of the free vibration of rectangular thinplates is given by double symplectic eigenfunction expansion method. | WANG Hua Alatancang HUANG Jun-Jie | 2009 | Communications in Theoretical Physics2009，52，12： | 7 |
| 5 | The separable Hamiltonian system and complete biorthogonal expansion method of Mindlin plate bending problems显示文摘A separable Hamiltonian system of Mindlin plate bending problems is obtained. Using the equivalence between the differential form and integral form of the separable Hamiltonian system, the biorthogonal relationships of the eigenfunctions are presented. Based on the biorthogonal relationships, a novel complete biorthogonal expansion of the Mindlin plate bending problems with two opposite sides simply supported is proposed through the products of operator matrices. The exact solutions to deflections and bending moments for the Mindlin plate with fully simply supported sides are obtained. A numerical example is illustrated to verify the accuracy and validity of the expansion method. | HOU GuoLin QI GaoWa XU YaNan CHEN Alatancang | 2013 | Science China(Physics,Mechanics & Astronomy)2013，56，5： | 5 |
| 6 | On symplectic self-adjointness of Hamiltonian operator matrices显示文摘Symplectic self-adjointness of Hamiltonian operator matrices is studied, which is important to 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 factorizations 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. | CHEN Alatancang JIN GuoHai WU DeYu | 2015 | Science China Mathematics2015，58，4： | 5 |
| 7 | Completeness of the System of Root Vectors of 2×2 Upper Triangular Infinite-Dimensional Hamiltonian Operators in Symplectic Spaces and Applications显示文摘The authors investigate the completeness of the system of eigen or root vectors of the 2×2 upper triangular infinite-dimensional Hamiltonian operator H 0.First,the geometrical multiplicity and the algebraic index of the eigenvalue of H0 are considered.Next,some necessary and sufficient conditions for the completeness of the system of eigen or root vectors of H0 are obtained.Finally,the obtained results are tested in several examples. | ALATANCANG | 2011 | Chinese Annals of Mathematics,Series B2011，32，6： | 4 |
| 8 | Invertibility of Infinite-Dimensional Hamiltonian Operators and Its Application to Plate Bending Equation显示文摘The results of invertibility and spectrum for some different classes of infinite-dimensional Hamiltonian operators,after a brief classification by domains,are given.By the above results,the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible.Furthermore,by a certain compactness,we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity,which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations. | Alatancang | 2008 | Communications in Theoretical Physics2008，49，3： | 2 |
| 9 | Symmetry of the Point Spectrum of Upper Triangular Infinite Dimensional Hamiltonian Operators显示文摘In this paper,by using characterization of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H,a necessary and sufficient condition is obtained on the symmetry of σp(A) and σp1(-A*) with respect to the imaginary axis.Then the symmetry of the point spectrum of H is given,and several examples are presented to illustrate the results. | WANG Hua Alatancang HUANG dun die | 2009 | Journal of Mathematical Research and Exposition2009，29，5： | 2 |
| 10 | Perturbation of Spectra for a Class of 2×2 Operator Matrices显示文摘In this paper,we study the perturbation of spectra for 2 × 2 operator matrices such as MX =(A X 0 B) and MZ =(A C Z B) on the Hilbert space H⊕K and the sets ∩X∈B(K,H) Pσ(MX),∩X∈B(K,H) R σ(MX) and ∩Z∈B(H,K) σ(MZ),∩Z∈B(H,K) Pσ(MZ),∩Z∈B(H,K) Rσ(MZ),∩Z∈B(H,K) Cσ(MZ),where R(C) is a closed subspace,are | ALATANCANG Guo-lin HOU Guo-jun HAI | 2012 | Acta Mathematicae Applicatae Sinica2012，28，4： | 2 |
| 11 | On feasibility of variable separation method on hamiltonian system for a class of plate bending equations显示文摘 | Eburilitu Alatancang | 2010 | Communication in Theoretical Physics2010，53，3： | 1 |
| 12 | Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators显示文摘 | Lin LI Alatancang CHEN De Yu WU | 2018 | Acta Mathematica Sinica,English Series2018，34，9： | 1 |
| 13 | Symmetry of the Point Spectrum of Infinite Dimensional Hamiltonian Operators and Its Applications显示文摘This paper studies the symmetry, with respect to the real axis, of the point spectrum of the upper triangular infinite dimensional Hamiltonian operator H. Note that the point spectrum of H can be described as σp(H) = σp(A) ∪σp1(-A*). Using the characteristic of the set σp1(-A*), we divide the point spectrum σp(A) of A into three disjoint parts. Then, a necessary and sufficient condition is obtained under which σp1(-A*) and one part of σp(A) are symmetric with respect to the real axis each other. Based on this result, the symmetry of σp(H) is completely given. Moreover, the above result is applied to thin plates on elastic foundation, plane elasticity problems and harmonic equations. | Hua WANG Alatancang Jun-jie HUANG | 2012 | Acta Mathematicae Applicatae Sinica2012，28，1： | 1 |
| 14 | Eigenvalue problem of a class of fourth-order Hamiltonian operators显示文摘The eigenvalue problem of a class of fourth-order Hamiltonian operators is studied. We first obtain the geometric multiplicity, the algebraic index and the algebraic multiplicity of each eigenvalue of the Hamiltonian operators. Then, some necessary and sufficient conditions for the completeness of the eigen or root vector system of the Hamiltonian operators are given, which is characterized by that of the vector system consisting of the first components of all eigenvectors. Moreover, the results are applied to the plate bending problem. | WANG Hua HUANG Jun-jie Alatancang | 2013 | Applied Mathematics(A Journal of Chinese Universities)2013，28，1： | 1 |
| 15 | The continuous spectrum of infinite dimensional Hamiltonian operators 显示文摘 | Huang Junjie Alatancang | 2006 | Mongolian Mathematical Journal2006，10，： | 1 |
| 16 | Invertibility of nonnegative Hamiltonian operator with unbounded entries显示文摘 | Wu D Y Alatancang | 2011 | J Math Anal App12011，373，： | 1 |
| 17 | Descriptions of spectra of infinite dimensional Hamilton operators and their applications显示文摘 | Huang J Alatancang Wu H | 2010 | Mathematische Nachrichten2010，283，8： | 1 |
| 18 | The continuous spectrum of infinite dimensional Hamiltonian operators显示文摘 | Huang Junjie Alatancang | 2006 | Mongolian Mathematical Journal2006，10，： | 1 |
| 19 | On the Point Spectrum and Non-Degenerate Symplectic Structure of Eigenfunction Systems of Off-Diagonal Infinite Dimensional Hamiltonian Operators显示文摘The point spectrum and non-degenerate symplectic structure of eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H=(■)are studied in this article.The necessary and sufficient conditions for the eigenfunction systems of off-diagonal infinite dimensional Hamiltonian operator H to have non-degenerate symplectic structure are given.Further,the necessary and sufficient conditions for point spectrum to be contained in real axis,imaginary axis and other areas are obtained for off-diagonal infinite dimensional Hamiltonian operator H,respectively.As an illustrating example,off-diagonal infinite dimensional Hamiltonian operators derived from the plate bending problem and string vibration problem are used to justify the conclusions. | Jie LIU Jiahui YU Alatancang CHEN | 2023 | Journal of Mathematical Research with Applications2023，43，6： | 0 |
| 20 | On Local Spectral Properties of Hamilton Type Operators显示文摘 | Jun-li SHEN Alatancang | 2018 | Acta Mathematicae Applicatae Sinica2018，34，1： | 0 |
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