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MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES
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作者 林孝盛 杨大春 +1 位作者 杨四辈 袁文 《Acta Mathematica Scientia》 SCIE CSCD 2024年第2期484-514,共31页
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 som... 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. 展开更多
关键词 Hardy space ball quasi-Banach function space Gaussian upper bound estimate non-negative self-adjoint operator maximal function
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Nonlinear Self-Adjointness, Conservation Laws and Soliton-Cnoidal Wave Interaction Solutions of(2+1)-Dimensional Modified Dispersive Water-Wave System 被引量:4
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作者 夏亚荣 辛祥鹏 张顺利 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第1期15-21,共7页
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 th... 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. 展开更多
关键词 MDWW system nonlinear self-adjointness conservation laws truncated Painlev′e analysis CTE method interaction solutions
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On the Self-adjointness of the Product Operators of Two mth-Order Differential Operators on [0,+∞) 被引量:5
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作者 JianYeAN JiongSUN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第5期793-802,共10页
In the present paper,the self-adjointness of the product of two ruth-order differential operators on [0,+∞)is studied.By means of the construction theory of self-adjoint operators and matrix computation,we obtain a s... In the present paper,the self-adjointness of the product of two ruth-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. 展开更多
关键词 self-adjointness PRODUCT Differential operators
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Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operators 被引量:1
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作者 Lin LI Alatancang CHEN De Yu WU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2018年第9期1473-1484,共12页
Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about sympl... Symplectic self-adjointness of infinite dimensional Hamiltonian operators is studied, the necessary and sufficient conditions are given. Using the relatively bounded perturbation, the sufficient conditions about symplectic self-adjointness are shown. 展开更多
关键词 Hamiltonian operator symplectic self-adjointness quadratic complement relative bound
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On the Essential Self-Adjointness of Pseudodifferential Operators
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作者 Fan Qihong Department of Mathematics Peking University Beijing,100871 China 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1994年第1期72-79,共8页
In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr(o|¨)dinger operator,-△+v(x),v(x)→-∞, as |x|→∞,and the relativistic co... In this paper we investigate the self-adjointness for a kind of pseudodifferential operators,which include the nonsemi-bounded Schr(o|¨)dinger operator,-△+v(x),v(x)→-∞, as |x|→∞,and the relativistic corrections to it,(-△+m<sup>2</sup>)<sup>1/2</sup>+v(x),v(x)→-∞,as|x|→∞. 展开更多
关键词 On the Essential self-adjointness of Pseudodifferential Operators
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On symplectic self-adjointness of Hamiltonian operator matrices 被引量:5
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作者 CHEN Alatancang JIN GuoHai WU DeYu 《Science China Mathematics》 SCIE CSCD 2015年第4期821-828,共8页
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 suffici... 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. 展开更多
关键词 symplectic elasticity symplectic self-adjoint Hamiltonian operator matrix
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On Self-Adjointness of the Product of Two Second-Order Differential Operators 被引量:3
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作者 D. E. Edmunds 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1999年第3期375-383,385-386,共11页
In this paper, the problem of self-adjointness of the product of two differential operators is considered. A number of results concerning self-adjointness of the product L<sub>2</sub>L<sub>1</sub&... In this paper, the problem of self-adjointness of the product of two differential operators is considered. A number of results concerning self-adjointness of the product L<sub>2</sub>L<sub>1</sub> of two second-order self-adjoint differential operators are obtained by using the general construction theory of self-adjoint extensions of ordinary differential operators. 展开更多
关键词 self-adjoint operator Differential operator Product of two differential operators
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Exactly Solvable Two-Parameter Models of Relativistic δ′s -Sphere Interactions in Quantum Mechanics
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作者 Jules Manirambona Juma Shabani Alfred Vyabandi 《Journal of Applied Mathematics and Physics》 2024年第4期1263-1285,共23页
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 ... 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. 展开更多
关键词 Boundary Conditions Problem -Sphere Interactions self-adjoint Operator Resolvent Equation Spectral Properties Scattering Theory
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A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED SELF-ADJOINT ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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作者 郭雯 林鹏程 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第3期231-241,共11页
In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniform... In this paper, based on the idea of El-Mistikawy and Werle[1] we construct a difference scheme for a singularly perturbed self-adjoint ordinary differential equation in conservation form. We prove that it is a uniformly convergent second order scheme. 展开更多
关键词 exp A UNIFORMLY CONVERGENT SECOND ORDER DIFFERENCE SCHEME FOR A SINGULARLY PERTURBED self-adjoint ORDINARY DIFFERENTIAL EQUATION IN CONSERVATION FORM
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AN APPLICATION OF THE EXPONENTIAL CUBIC SPLINES TO NUMERICAL SOLUTION OF A SELF-ADJOINT PERTURBATION PROBLEM
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作者 Mirjana Stojanovic 《Analysis in Theory and Applications》 1998年第2期38-43,共6页
We present a class of the second order optimal splines difference schemes derived from ex- ponential cubic splines for self-adjoint singularly perturbed 2-point boundary value problem. We prove an optimal error estima... We present a class of the second order optimal splines difference schemes derived from ex- ponential cubic splines for self-adjoint singularly perturbed 2-point boundary value problem. We prove an optimal error estimate and give illustrative numerical example. 展开更多
关键词 exp AN APPLICATION OF THE EXPONENTIAL CUBIC SPLINES TO NUMERICAL SOLUTION OF A self-adjoint PERTURBATION PROBLEM
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Helmholtz Decomposition of Vector Fields Using an Optimal Preconditioned Conjugate Gradient Algorithm
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作者 Jorge Lopez 《Journal of Applied Mathematics and Physics》 2023年第5期1337-1348,共12页
In this article, we study numerically a Helmholtz decomposition methodology, based on a formulation of the mathematical model as a saddle-point problem. We use a preconditioned conjugate gradient algorithm, applied to... In this article, we study numerically a Helmholtz decomposition methodology, based on a formulation of the mathematical model as a saddle-point problem. We use a preconditioned conjugate gradient algorithm, applied to an associated operator equation of elliptic type, to solve the problem. To solve the elliptic partial differential equations, we use a second order mixed finite element approximation for discretization. We show, using 2-D synthetic vector fields, that this approach, yields very accurate solutions at a low computational cost compared to traditional methods with the same order of approximation. 展开更多
关键词 Helmholtz Decomposition self-adjoint Operator Optimal Preconditioning Finite Element
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Conservation laws of the generalized short pulse equation
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作者 张智勇 陈玉福 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第2期12-15,共4页
We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution.Moreover,any adjoint symmetry is a differential substitution of nonlinear self-adjointness,and vice versa.Co... We show that the generalized short pulse equation is nonlinearly self-adjoint with differential substitution.Moreover,any adjoint symmetry is a differential substitution of nonlinear self-adjointness,and vice versa.Consequently,the general conservation law formula is constructed and new conservation laws for some special cases are found. 展开更多
关键词 nonlinear self-adjointness with differential substitution adjoint symmetry conservation law
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BOUNDEDNESS OF STEIN'S SQUARE FUNCTIONS ASSOCIATED TO OPERATORS ON HARDY SPACES 被引量:1
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作者 闫雪芳 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期891-904,共14页
Let (X, d,μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2(X). Assume that the semigroup e^-tL ge... Let (X, d,μ) be a metric measure space endowed with a metric d and a nonnegative Borel doubling measure μ. Let L be a second order non-negative self-adjoint operator on L^2(X). Assume that the semigroup e^-tL generated by L satisfies the Davies-Gaffney estimates. Also, assume that L satisfies Plancherel type estimate. Under these conditions, we show that Stein's square function Gδ(L) arising from Bochner-Riesz means associated to L is bounded from the Hardy spaces HL^p(X) to L^p(X) for all 0 〈 p ≤ 1. 展开更多
关键词 Stein's square function non-negative self-adjoint operator Hardy spaces Davies- Gaffney estimate Plancherel type estimate
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Simulation of detection and scattering of sound waves by the lateral line of a fish
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作者 V M Adamyan I Y Popov +1 位作者 I V Blinova V V Zavalniuk 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第2期398-404,共7页
A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressure... A solvable model of lateral line of a fish based on a wave equation with additional boundary conditions on a set of isolated points is proposed.Within the framework of this model it is shown that the ratio of pressures on lateral lines on different fish flanks,as well as the cross section of sound scattering on both the lines,strongly depends on angles of incidence of incoming sound waves.The strong angular dependence of the pressure ratio seems to be sufficient for the fish to determine the directions from which the sound is coming. 展开更多
关键词 acoustic equation point self-adjoint perturbations of Laplace operator SCATTERING lateral line
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Positive-Definite Operator-Valued Kernels and Integral Representations
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作者 L. Lemnete-Ninulescu 《Applied Mathematics》 2012年第12期1990-1999,共10页
A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary... A truncated trigonometric, operator-valued moment problem in section 3 of this note is solved. Let be a finite sequence of bounded operators, with arbitrary, acting on a finite dimensional Hilbert space H. A necessary and sufficient condition on the positivity of an operator kernel for the existence of an atomic, positive, operator-valued measure , with the property that for every with , the moment of coincides with the term of the sequence, is given. The connection between some positive definite operator-valued kernels and the Riesz-Herglotz integral representation of the analytic on the unit disc, operator-valued functions with positive real part in the class of operators in Section 4 of the note is studied. 展开更多
关键词 Unitary-Operator self-adjoint OPERATOR Joint SPECTRAL Measure of a COMMUTING TUPLE of Operators SPECTRAL Projector Complex Moments Analytic Vectorial Functions
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Error Estimations, Error Computations, and Convergence Rates in FEM for BVPs
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作者 Karan S. Surana A. D. Joy J. N. Reddy 《Applied Mathematics》 2016年第12期1359-1407,共49页
This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential o... This paper presents derivation of a priori error estimates and convergence rates of finite element processes for boundary value problems (BVPs) described by self adjoint, non-self adjoint, and nonlinear differential operators. A posteriori error estimates are discussed in context with local approximations in higher order scalar product spaces. A posteriori error computational framework (without the knowledge of theoretical solution) is presented for all BVPs regardless of the method of approximation employed in constructing the integral form. This enables computations of local errors as well as the global errors in the computed finite element solutions. The two most significant and essential aspects of the research presented in this paper that enable all of the features described above are: 1) ensuring variational consistency of the integral form(s) resulting from the methods of approximation for self adjoint, non-self adjoint, and nonlinear differential operators and 2) choosing local approximations for the elements of a discretization in a subspace of a higher order scalar product space that is minimally conforming, hence ensuring desired global differentiability of the approximations over the discretizations. It is shown that when the theoretical solution of a BVP is analytic, the a priori error estimate (in the asymptotic range, discussed in a later section of the paper) is independent of the method of approximation or the nature of the differential operator provided the resulting integral form is variationally consistent. Thus, the finite element processes utilizing integral forms based on different methods of approximation but resulting in VC integral forms result in the same a priori error estimate and convergence rate. It is shown that a variationally consistent (VC) integral form has best approximation property in some norm, conversely an integral form with best approximation property in some norm is variationally consistent. That is best approximation property of the integral form and the VC of the integral form is equivalent, one cannot exist without the other, hence can be used interchangeably. Dimensional model problems consisting of diffusion equation, convection-diffusion equation, and Burgers equation described by self adjoint, non-self adjoint, and nonlinear differential operators are considered to present extensive numerical studies using Galerkin method with weak form (GM/WF) and least squares process (LSP) to determine computed convergence rates of various error norms and present comparisons with the theoretical convergence rates. 展开更多
关键词 Finite Element Error Estimation Convergence Rate A Priori A Posteriori BVP Variationally Consistent Integral Form Variationally Inconsistent Integral Form Differential Operator Classification self-adjoint NON-self-adjoint Nonlinear
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The Third Kind Of Particles
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作者 ShaoXu Ren 《Journal of Modern Physics》 2014年第9期800-869,共70页
There are two kinds of spin particles in nature, the Boson and the Fermion.(For more information, please refere to the PDF.)
关键词 The THIRD KIND Of Particles TKP Boson Fermion HERMITIAN MATRICES NON-HERMITIAN MATRICES HERMITIAN self-adjoint positive definite NON-HERMITIAN self-adjoint finite dimensional MATRICES infinite dimensional MATRICES
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Singular Value Inequalities for Compact Normal Operators
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作者 Wasim Audeh 《Advances in Linear Algebra & Matrix Theory》 2013年第4期34-38,共5页
We give singular value inequality to compact normal operators, which states that if is compact normal operator on a complex separable Hilbert space, where is the cartesian decomposition of , then Moreover, we give ine... We give singular value inequality to compact normal operators, which states that if is compact normal operator on a complex separable Hilbert space, where is the cartesian decomposition of , then Moreover, we give inequality which asserts that if?is compact normal operator, then .Several inequalities will be proved. 展开更多
关键词 COMPACT OPERATOR INEQUALITY Normal OPERATOR self-adjoint OPERATOR SINGULAR Value
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More Results on Singular Value Inequalities for Compact Operators
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作者 Wasim Audeh 《Advances in Linear Algebra & Matrix Theory》 2013年第4期27-33,共7页
The well-known arithmetic-geometric mean inequality for singular values, according to Bhatia and Kittaneh, says that if and are compact operators on a complex separable Hilbert space, then Hirzallah has proved that if... The well-known arithmetic-geometric mean inequality for singular values, according to Bhatia and Kittaneh, says that if and are compact operators on a complex separable Hilbert space, then Hirzallah has proved that if are compact operators, then We give inequality which is equivalent to and more general than the above inequalities, which states that if are compact operators, 展开更多
关键词 Compact OPERATOR INEQUALITY POSITIVE OPERATOR self-adjoint OPERATOR SINGULAR Value
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The Definition of Universal Momentum Operator of Quantum Mechanics and the Essence of Micro-Particle’s Spin——To Reveal the Real Reason That the Bell Inequality Is Not Supported by Experiments
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作者 Xiaochun Mei Ping Yu 《Journal of Modern Physics》 2012年第6期451-470,共20页
The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to ca... The definition of momentum operator in quantum mechanics has some foundational problems and needs to be improved. For example, the results are different in general by using momentum operator and kinetic operator to calculate microparticle’s kinetic energy. In the curved coordinate systems, momentum operators can not be defined properly. When momentum operator is acted on non-eigen wave functions in coordinate space, the resulting non-eigen values are complex numbers in general. In this case, momentum operator is not the Hermitian operator again. The average values of momentum operator are complex numbers unless they are zero. The same problems exist for angle momentum operator. Universal momentum operator is proposed in this paper. Based on it, all problems above can be solved well. The logical foundation of quantum mechanics becomes more complete and the EPY momentum paradox can be eliminated thoroughly. By considering the fact that there exist a difference between the theoretical value and the real value of momentum, the concepts of auxiliary momentum and auxiliary angle momentum are introduced. The relation between auxiliary angle momentum and spin is deduced and the essence of micro-particle’s spin is revealed. In this way, the fact that spin gyro-magnetic ratio is two times of orbit gyro-magnetic ratio, as well as why the electrons of ground state without obit angle momentum do not fall into atomic nuclear can be explained well. The real reason that the Bell inequality is not supported by experiments is revealed, which has nothing to do with whether or not hidden variables exist, as well as whether or not locality is violated in microcosmic processes. 展开更多
关键词 Quantum Mechanics UNIVERSAL MOMENTUM OPERATOR UNIVERSAL Angle MOMENTUM OPERATOR Hermitian OPERATOR self-adjoint OPERATOR SPIN Bell INEQUALITY Hidden Variables
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