MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

Exactly Solvable Two-Parameter Models of Relativistic δ′s -Sphere Interactions in Quantum Mechanics

We make a systematic study of two-parameter models of δ ′ s -sphere interaction and δ ′ s -sphere plus a Coulomb interaction. Where δ ′ s interaction denotes the δ ′ -sphere interaction of the second kind. We provide the mathematical definitions of Hamiltonians and obtain new results for both models, in particular the resolvents equations, spectral properties and some scattering quantities.

The order-preserving convergence for spectral approximation of self-adjoint completely continuous operators

This paper discusses the order-preserving convergence for spectral approximation of the self-adjoint completely continuous operator T.Under the condition that the approximate operator Th converges to T in norm,it is proven that the k-th eigenvalue of Th converges to the k-th eigenvalue of T.(We sorted the positive eigenvalues in decreasing order and negative eigenvalues in increasing order.) Then we apply this result to conforming elements,nonconforming elements and mixed elements of self-adjoint elliptic differential operators eigenvalue problems,and prove that the k-th approximate eigenvalue obtained by these methods converges to the k-th exact eigenvalue.

Nonlinear Self-Adjointness, Conservation Laws and Soliton-Cnoidal Wave Interaction Solutions of(2+1)-Dimensional Modified Dispersive Water-Wave System

This paper mainly discusses the(2+1)-dimensional modified dispersive water-wave(MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlev′e analysis and consistent tanh-function expansion(CTE)method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved.

On Self-Adjointness of the Product of Two Second-Order Differential Operators

In this paper, the problem of self-adjointness of the product of two differential operators isconsidered. A number of results concerning self-adjointness of the product L2L1 of two second-orderself-adjoint differential operators are obtained by using the general construction theory of self-adjointextensions of ordinary differential operators.

Decomposition of almost Poisson structure of non-self-adjoint dynamical systems

Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.

Variable integral and smooth exponent Besov spaces associated to non-negative self-adjoint operators

We introduce the variable integral and the smooth exponent Besov spaces associated to non-negative self-adjoint operators.Then we give the equivalent norms via the Peetre type maximal functions and atomic decomposition of these spaces.

Numerical study of self-adjoint singularly perturbed two-point boundary value problems using collocation method with error estimation

A numerical treatment for self-adjoint singularly perturbed second-order two-point boundary value problems using trigonometric quintic B-splines is presented,which depend on different engineering applications.The method is found to have a truncation error of O(h 6)and converges to the exact solution at O(h 4).The numerical examples show that our method is very effective and the maximum absolute error is acceptable.

ON SELF-ADJOINTNESS OF THE PRODUCT OF TWO n-ORDER DIFFERENTIAL OPERATORS ON[a,b]

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On the Essential Self-Adjointness of Pseudodifferential Operators

In this paper we investigate the self-adjointness for a kind of pseudodifferentialoperators,which include the nonsemi-bounded Schr（o|¨）dinger operator,-△+v（x）,v（x）→-∞,as |x|→∞,and the relativistic corrections to it,（-△+m2）1/2+v（x）,v（x）→-∞,as|x|→∞.

On the Norm of a Self-Adjoint Operator and a New Bilinear Integral Inequality

在这篇论文，自我伴随积分操作员 T 的标准的表示：L^2 (0，∞) → L^2 (0，∞) 被获得。作为应用，有一个最好的经常的因素的新双线性的不可分的不平等被建立，一些特别盒子被考虑。

On symplectic self-adjointness of Hamiltonian operator matrices

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.

On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0,+∞)

In the present paper, the self-adjointness of the product of two mth-order differential operators on [0, ∞) is studied. By means of the construction theory of self-adjoint operators and matrix computation, we obtain a sufficient and necessary condition to ensure that the product operator is self-adjoint, which extends the results in the second order case.

Universal Inequalities for Lower Order Eigenvalues of Self-Adjoint Operators and the Poly-Laplacian

In this paper,we first establish an abstract inequality for lower order eigenvalues of a self-adjoint operator on a Hilbert space which generalizes and extends the recent results of Cheng et al.(Calc.Var.Partial Diferential Equations,38,409-416(2010)).Then,making use of it,we obtain some universal inequalities for lower order eigenvalues of the biharmonic operator on manifolds admitting some special functions.Moreover,we derive a universal inequality for lower order eigenvalues of the poly-Laplacian with any order on the Euclidean space.

ADJACENCY PRESERVING MAPS ON THE SPACE OF SELF-ADJOINT OPERATORS

The authors extend Hua’s fundamental theorem of the geometry of Hermitian matri- ces to the in?nite-dimensional case. An application to characterizing the corresponding Jordan ring automorphism is also presented.

Maps Preserving Numerical Radius or Cross Norms of Products of Self-adjoint Operators

让 H 是有暗淡 H 鈮 ? 的一个复杂 Hilbert 空格 3， B s (H)( 真实) H 上的所有自我伴随操作符的乔丹代数学。每 surjective 地图桅：保存操作员产品的数字半径的 B s (H) 鈫 ? B s (H)( 分别地，乔丹三元组产品) 被描绘。保存操作员产品的一个生气操作员标准的 B s (H) 上的 surjective 地图的描述(分别地操作员的乔丹三元组产品) 也被给。自我伴随操作员的关键词空间-数字半径-操作员先生( 2000 )题目分类 47H20 的产品- 47B49 - 47A12 由中国的国家科学基金支持了(同意Nos. 10771157 ， 10871111 )，山西(资助号码 2007011016 )和为归还学者(资助号码 2007-38 )

A PRIORI AND A POSTERIORI ERROR ESTIMATES OF A WEAKLY OVER-PENALIZED INTERIOR PENALTY METHOD FOR NON-SELF-ADJOINT AND INDEFINITE PROBLEMS

在这份报纸，我们为 non-self-adjoint 和不定的问题学习一个弱过去惩罚的内部惩罚方法。一最佳在精力标准的 priori 错误估计被导出。另外，我们介绍一基于剩余一个 posteriori 错误评估者，它被证明在精力标准可靠、有效。一些数字睾丸被介绍验证我们的理论分析。[从作者抽象]

Fredholm Index and Spectral Flow in Non-self-adjoint Case

A version of the "Fredholm index = spectral flow" theorem is proved for general families of elliptic operators {A(t)} t∈R on closed (compact and without boundary) manifolds. Here we do not require that A(t), t∈R or its leading part is self-adjoint.