Self Adjoint Operators(自伴随算子)研究综述
Self Adjoint Operators 自伴随算子 - This problem is described by a quadratic operator polynomial with self-adjoint operators. [1] For any multi-graph $G$ with edge weights and vertex potential, and its universal covering tree ${\mathcal{T}}$, we completely characterize the point spectrum of operators $A_{{\mathcal{T}}}$ on ${\mathcal{T}}$ arising as pull-backs of local, self-adjoint operators $A_{G}$ on $G$. [2] We generalize Moore’s nonstandard proof of the Spectral theorem for bounded self-adjoint operators to the case of unbounded operators. [3] 41 , 613–639 ( 2002 ), creates a topos of presheaves over the poset V ( N ) $\mathcal {V}(\mathcal {N})$ of Abelian von Neumann subalgebras of the von Neumann algebra N $\mathcal {N}$ of bounded operators associated to a physical system, and established several results, including: (a) a connection between the Kochen-Specker theorem and the non-existence of a global section of the spectral presheaf; (b) a version of the spectral theorem for self-adjoint operators; (c) a connection between states of N $\mathcal {N}$ and measures on the spectral presheaf; and (d) a model of dynamics in terms of V ( N ) $\mathcal {V}(\mathcal {N})$. [4] The objective of this paper is to reveal an operator version of the Jensen inequality and its reverse one for s-convex functions and self-adjoint operators on a Hilbert space. [5] We study sufficient conditions that guarantee the boundedness of a C 0 -semigroup of operators on a Hilbert space whose generator can be decomposed as a product of self-adjoint operators. [6] Examples of the negative definite self-adjoint operators include fractional powers of the Laplacian, i. [7] We investigate eigenvalue perturbations for a class of infinite tridiagonal matrices which define unbounded self-adjoint operators with discrete spectrum. [8] This leads to the representation of physical observables through stochastic processes instead of self-adjoint operators. [9] The integral representation is obtained for a family of bounded commutative self-adjoint operators which are connected by algebraic relationship. [10] The use of tools of the theory of spaces of Hilbert, the spectral theory for unbounded self-adjoint operators, Sturm–Liouville’s theory, variational methods, analytic perturbation theory of operators, and the extension theory of symmetric operators are pieces fundamental in our study. [11] To simplify exposition we consider here self-adjoint operators. [12] The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. [13] Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. [14] Non-self-adjoint operators have many applications, including quantum and heat equations. [15] These results will be connected with the study of the ground state energy of two remarkable three-dimensional self-adjoint operators, studied in depth in Albeverio’s monograph, perturbed by an attractive δ-distribution supported on the spherical shell of radius r0. [16] Different self-adjoint operators can lead to new classes of M-indeterminate densities. [17] It is proved that for any $\gamma \in \mathbb{C}$, $|\gamma| = 1$, the operator $\gamma I$ can be represented as the product of four unitary self-adjoint operators. [18] We find supersymmetric partners of a family of self-adjoint operators which are self-adjoint extensions of the differential operator −d/dx on L[−a, a], a > 0, that is, the one dimensional infinite square well. [19] Using the resolvent operator, we develop an algorithm for computing smoothed approximations of spectral measures associated with self-adjoint operators. [20] Here, motivated by the spreading interest in non self-adjoint operators in quantum mechanics, we extend this situation to a set of four operators, c, d, r and s, satisfying dc = rs + γ 1 and cd = sr + δ 1 , and we show that they are also ladder operators. [21] We study generic fractal properties of bounded self-adjoint operators through lower and upper generalized fractal dimensions of spectral measures. [22] The main step of their proof is a new method to study the spectral properties of non-self-adjoint operators in the semiclassical regime. [23] While it is known that the distributive law does not apply to quantum logic, and the equality axiom turns out not to hold in quantum set theory, he showed that the real numbers in quantum set theory are in one-to-one correspondence with the self-adjoint operators on a Hilbert space, or equivalently the physical quantities of the corresponding quantum system. [24] A common assumption in non-relativistic quantum mechanics is that self-adjoint operators mathematically represent properties of quantum systems. [25] As well as being particularly simple, it generalises previous no-signalling conditions in that it allows for degeneracies and can be applied to all bounded self-adjoint operators. [26] To prove this, we use the $$L_1 $$ -functional calculus for self-adjoint operators and a suitable similarity transformation. [27] The variation of spectral subspaces for linear self-adjoint operators under an additive bounded perturbation is considered. [28] The study of the solvability of this problem is based on the spectral theory of compact self-adjoint operators. [29] These fractional-order governing equations involve self-adjoint operators and admit unique solutions, in contrast to analogous studies following the local Cauchy’s hypothesis. [30] We show that for any $(n+1)$-tuple ${\bf A}$ of bounded self-adjoint operators the multiple operator integral $T_{a^{[n]}}^{\bf A}$ maps $\mathcal{S}_{p_1} \times \ldots \times \mathcal{S}_{p_n}$ to $\mathcal{S}_{1, \infty}$ boundedly with uniform bound in ${\bf A}$. [31] Several recent papers have focused their attention in proving the correct analogue to the Lieb-Thirring inequalities for non self-adjoint operators and in finding bounds on the distribution of their eigenvalues in the complex plane. [32] The aim of this short note is to study the kinematics of this noncommutative space using the tools developed for usual quantum mechanics, namely quantize the space associating to it an algebra of operators, obtain a concrete representation of them on some Hilbert space, whose vectors are pure states, diagonalize sets of completely commuting observables and use the known measurement theory, namely that the possible results of a measurement are given by the eigenvalues of the observables with probabilities given by the spectral decomposition of self-adjoint operators. [33] $ Similar properties are valid for evolution equations of the form $$ u''+ cu' + (B+A(t))u = 0$$ where $A(t) $ and $B$ are self-adjoint operators on a real Hilbert space $H$ with $B$ coercive and $A(t)$ bounded in $L(H)$ with a sufficiently small bound of its norm in $L^{\infty}(R+, L(H))$. [34] Chiappinelli concerning the local persistence property of the unit eigenvectors of perturbed self-adjoint operators in a real Hilbert space. [35] It is shown that these problems generate self-adjoint operators. [36] Livshits on the spectral decomposition of linear non-self-adjoint operators, as well as on the sectoriality of the fractional differentiation operator. [37] The last section is devoted to symmetric operators and self-adjoint operators. [38] In this paper we prove spectral multiplier theorems for abstract self-adjoint operators on spaces of homogeneous type. [39] 41 , 613–639 ( 2002 ), creates a topos of presheaves over the poset V ( N ) $\mathcal {V}(\mathcal {N})$ of Abelian von Neumann subalgebras of the von Neumann algebra N $\mathcal {N}$ of bounded operators associated to a physical system, and established several results, including: (a) a connection between the Kochen-Specker theorem and the non-existence of a global section of the spectral presheaf; (b) a version of the spectral theorem for self-adjoint operators; (c) a connection between states of N $\mathcal {N}$ and measures on the spectral presheaf; and (d) a model of dynamics in terms of V ( N ) $\mathcal {V}(\mathcal {N})$. [40] They launched this theory in order to compute the derivative of the function t↦f(A(t)), where {A(t)}t is a family of bounded self-adjoint operators depending on the parameter t. [41] It is proved that in a quite general setting, generalized weighted quasi-arithmetic means on self-adjoint operators are not monotone in their variables which is an interesting property. [42] We establish the following results on higher order $\mathcal{S}^p$-differentiability, $1这个问题由具有自伴随算子的二次算子多项式来描述。 [1] 对于任何具有边权重和顶点势的多图 $G$ 及其通用覆盖树 ${\mathcal{T}}$，我们完全刻画了算子 $A_{{\mathcal{T}}}$ 的点谱在 ${\mathcal{T}}$ 上，由于 $G$ 上的本地自伴算符 $A_{G}$ 的回调而产生。 [2] 我们将摩尔关于有界自伴算子的谱定理的非标准证明推广到无界算子的情况。 [3] 41 , 613–639 (2002)，在冯诺依曼代数 N $\mathcal { N}$ 个与物理系统相关的有界算子，并建立了几个结果，包括： (b) 自伴算子的谱定理的一个版本； (c) N $\mathcal {N}$ 的状态与谱前层测量之间的联系； (d) 根据 V ( N ) $\mathcal {V}(\mathcal {N})$ 的动力学模型。 [4] 本文的目的是揭示 Jensen 不等式的一个算子版本及其在希尔伯特空间上的 s-凸函数和自伴算子的逆版本。 [5] 我们研究了保证在希尔伯特空间上的 C 0 算子半群的有界性的充分条件，其生成器可以分解为自伴算子的乘积。 [6] 负定自伴算子的例子包括拉普拉斯算子的分数幂，即。 [7] 我们研究了一类无限三对角矩阵的特征值扰动，该矩阵定义了具有离散谱的无界自伴随算子。 [8] 这导致通过随机过程而不是自伴随算子来表示物理可观察量。 [9] 通过代数关系连接的有界交换自伴算子族得到了积分表示。 [10] 希尔伯特空间理论工具的使用、无界自伴算子的谱理论、Sturm-Liouville 理论、变分方法、算子的解析微扰理论和对称算子的可拓理论是我们研究的基础。 [11] 为了简化说明，我们在这里考虑自伴算子。 [12] 本文的目的是建立具有自伴随算子的时间分数伪抛物方程的直接和反问题的可解性结果。 [13] 量子力学中的可观测量由希尔伯特空间上的自伴算子表示。 [14] 非自伴算子有很多应用，包括量子和热方程。 [15] 这些结果将与 Albeverio 的专着中深入研究的两个显着的 3 维自伴算子的基态能量研究相关联，这些算子受到半径 r0 球壳上的有吸引力的 δ 分布的干扰。 [16] 不同的自伴算子可以导致新的 M-不定密度类别。 [17] 证明对于任何 $\gamma \in \mathbb{C}$, $|\gamma| = 1$，算子 $\gamma I$ 可以表示为四个酉自伴算子的乘积。 [18] 我们找到了自伴算子家族的超对称伙伴，它们是微分算子 -d/dx 在 L[-a, a], a > 0 上的自伴扩展，即一维无限平方阱。 [19] 使用分解算子，我们开发了一种算法，用于计算与自伴随算子相关的频谱测量的平滑近似值。 [20] 在这里，由于对量子力学中非自伴算子的广泛兴趣，我们将这种情况扩展到一组四个算子，c、d、r 和 s，满足 dc = rs + γ 1 和 cd = sr + δ 1 ，并且我们证明他们也是梯形图运算符。 [21] 我们通过谱度量的下广义分形维数研究有界自伴算子的一般分形性质。 [22] 他们证明的主要步骤是一种研究半经典状态下非自伴算子谱性质的新方法。 [23] 虽然已知分配律不适用于量子逻辑，并且等式公理在量子集合论中不成立，但他证明了量子集合论中的实数与自我一一对应-希尔伯特空间上的伴随算子，或等价于相应量子系统的物理量。 [24] 非相对论量子力学中的一个常见假设是自伴随算子在数学上表示量子系统的属性。 [25] 除了特别简单之外，它还概括了以前的无信号条件，因为它允许退化并且可以应用于所有有界自伴随算子。 [26] 为了证明这一点，我们使用 $$L_1 $$ - 自伴算子的泛函演算和 合适的相似变换。 [27] 考虑了加性有界扰动下线性自伴算子谱子空间的变化。 [28] 该问题的可解性研究基于紧自伴算子的谱理论。 [29] 这些分数阶控制方程涉及自伴随算子并承认唯一解，这与遵循局部柯西假设的类似研究相反。 [30] 我们证明，对于任何有界自伴算子的 $(n+1)$-元组 ${\bf A}$，多重算子积分 $T_{a^{[n]}}^{\bf A}$ 映射$\mathcal{S}_{p_1} \times \ldots \times \mathcal{S}_{p_n}$ 到 $\mathcal{S}_{1, \infty}$ 有界，在 ${\bf一个}$。 [31] 最近的几篇论文将他们的注意力集中在证明非自伴算子的 Lieb-Thirring 不等式的正确模拟上，并在复平面上寻找其特征值分布的界限。 [32] 这篇简短笔记的目的是使用为通常的量子力学开发的工具来研究这个非对易空间的运动学，即将与其相关的空间量化为算子的代数，在某个希尔伯特空间上获得它们的具体表示，其向量为纯状态，对完全可交换的可观测量集进行对角化，并使用已知的测量理论，即测量的可能结果由可观测量的特征值给出，概率由自伴算子的谱分解给出。 [33] nan [34] nan [35] nan [36] nan [37] nan [38] nan [39] nan [40] nan [41] nan [42] nan [43] nan [44] nan [45] nan [46] nan [47] nan [48] nan [49] nan [50]