混合气体线性化Boltzmann算子的特征值与特征函数

考虑了混合气体线性化Boltzmann算子的特征值与特征函数问题.通过对算子中核函数的分析得出了更一般的混合气体线性化Boltzmann算子的特征值与特征函数.而且结论还适用于单一气体情况.     

The Point Spectrum of the Linearized Boltzmann Operator with the External-force Term in a Bounded Domain

We will investigate the point spectrum on the imaginary axis of the linearized Boltzmann operator with an external-force potential in a bounded domain whose boundary is sufficiently smooth. The boundary condition considered is the perfectly reflective boundary condition. The point spectrum on the imaginary axis is only equal to {0}. However, the null space varies with the common axes of symmetry of the domain and the external-force potential.     

The Lower Weyl Spectrum of a Positive Operator

For the lower Weyl spectrum $$\sigma_{\rm w}^-(T) = \bigcap_{0 \le K \in \mathcal{K}(E) \le T} \sigma(T - K),$$ where T is a positive operator on a Banach lattice E, the conditions for which the equality ${\sigma_{\rm w}^-(T) = \sigma_{\rm w}^-(T^*)}$ holds, are established. In particular, it is true if E has order continuous norm. An example of a weakly compact positive operator T on ? _∞ such that the spectral radius ${r(T) \in \sigma_{\rm w}^-(T) {\setminus} (\sigma_{\rm f}(T) \cup \sigma_{\rm w}^-(T^*))}$ , where σ _f(T) is the Fredholm spectrum, is given. The conditions which guarantee the order continuity of the residue T _?1 of the resolvent R(., T) of an order continuous operator T ≥ 0 at ${r(T) \notin \sigma_{\rm f}(T)}$ , are discussed. For example, it is true if T is o-weakly compact. It follows from the proven results that a Banach lattice E admitting an order continuous operator T ≥ 0, ${r(T) \notin \sigma_{\rm f}(T)}$ , can not have the trivial band ${E_n^\sim}$ of order continuous functionals in general. It is obtained that a non-zero order continuous operator T : E → F can not be approximated in the r-norm by the operators from ${E_\sigma^\sim \otimes F}$ , where F is a Banach lattice, ${E_\sigma^\sim}$ is a disjoint complement of the band ${E_n^\sim}$ of E*.     

一类线性非自伴算子的谱

近年来国际上出现了一类以迁移理论为背景的所谓＂ｕ－标算子（ｕ－ｓｃａｌａｒｏｐｅｒａｔｏｒ）＂．本文研究ｕ－标算子与经典的标型谱算子（ｓｐｅｃｔｒａｌｏｐｅｒａｔｏｒｏｆｓｃａｌａｒｔｙｐｅ）的内在联系，给出了此类算子的谱与其无界投影族之间的关系，证明了该类算子的剩余谱是空集．     

Integral Formulas for the r-Mean Curvature Linearized Operator of a Hypersurface

For a normal variation of a hypersurface M ⁿ in a space form Q _c ⁿ⁺¹ by a normal vector field fN, R. Reilly proved:

The Generic Local Spectrum of Any Operator is The Full Spectrum

Let T=(T₁, ..., T_n) be a commuting n-tuple of bounded linearoperators acting on some complex Banach space X. We show thatif T has the single-valued extension property, then the localspectrum _T(x) coincides with the spectrum (T), for all vectorsx X, except on a set of the first Baire category. 1991 MathematicsSubject Classification 47A11, 47A13.     

2n阶J-自伴向量微分算子的本质谱

利用算子直和分解的方法研究了2n阶J-自伴向量微分算子的本质谱,得到了这类算子的本质谱的分布范围.     

一类带抽象边界条件的迁移算子的谱

在Lp(1≤p＜+∞)空间中,研究了板几何中一类带抽象边界条件的各向异性、连续能量、均匀介质的迁移方程,利用豫解算子方法,得到了该迁移算子的谱在区域Γε中仅由有限个具有限代数重数的离散本征值组成.     

一类广义 Schrodinger 算子的自伴性与本质谱

本文在一类Lp位势V(x)下建立了广义Schrodinger算子H=(-△)m+V(x)在C000(Rn)上的本质自伴性,给出了H的本质谱的分布.     

On Absolute Continuity of the Spectrum of a 3D Periodic Magnetic Dirac Operator

Absolute continuity of the spectrum of a 3D periodic magnetic Dirac operator is proved provided that the magnetic potential A belongs to the space \({H^q_{\mathrm{loc}},q >1 }\) , and the matrix potential \({\widehat V\in L^3_{\mathrm {loc}}}\) is represented in the form \({\widehat V=\widehat V_0+\widehat V_1}\) , where \({\widehat V_0}\) commutes and \({\widehat V_1}\) anticommutes with the Dirac matrices \({\widehat \alpha _j, j = 1, 2, 3}\) .     

The Spectrum of a Parametrized Partial Differential Operator Occurring in Hydrodynamics

A partial differential operator associated with natural oscillationsof an incompressible fluid in the neighbourhood of an ellipticalflow is considered. The differentiation is only taken with respectto the angular variable, and thus the operator becomes a familyof ordinary differential operators parametrized by the radialvariable. It is shown that the spectra of these ordinary differentialoperators completely determine the spectrum of the given operatorwhich turns out to have a kind of skeleton structure.     

On the Spectrum of a Non-Self-Adjoint Quasiperiodic Operator

Doklady Mathematics - We study the operator $$\mathcal{A}$$ acting in $${{l}^{2}}(\mathbb{Z})$$ by the formula $${{(\mathcal{A}u)}_{l}} = {{u}_{{l + 1}}} + {{u}_{{l - 1}}} + \lambda {{e}^{{ - 2\pi...     

Spectrum of a Self-Adjoint Operator and Palais-Smale Conditions

The spectrum and essential spectrum of a self-adjoint operatorin a real Hilbert space are characterized in terms of Palais–Smaleconditions on its quadratic form and Rayleigh quotient respectively.     

Homogenization of the Euler system in a 2D porous medium

We study the homogenization of the Euler system in a periodic porous medium (of period ɛ) by using the notion of two-scale convergence. At the limit, we recover a system which couples a cell problem with the macroscopic one.     

算子的算子点谱的判定

本文讨论了算子Ａ∈Ｂ（Ｈ）_Ｎ为算子Ｔ∈Ｂ（Ｈ）的算子点谱的判定条件,特别得到：当Ｔ为亚正常算子时,Ａ为Ｔ的算子点谱的判定条件,另外还得到ｋｅｒτ^ｎ_Ｔ,Ａ＝ｋｅｒτ_Ｔ,Ａ成立的充分条件     

算子的算子点谱的判定

本文讨论了算子A∈B(H)     

一类广义Schrdinger算子的自伴性与本质谱

本文在一类 Ｌｐ位势Ｖ（ｘ）下建立了广义Ｓｃｈｒｏｄｉｎｇｅｒ算子Ｈ＝（－Δ）ｍ＋Ｖ（ｘ）在Ｃ∞０（Ｒｎ）上的本质自伴性，给出了Ｈ的本质谱的分布．